In the local, unramified case the determinantal functions associated to the group-ring of a finite group satisfy Galois descent. This note examines the obstructions to Galois determinantal descent in the ramified case.

of function fields and Hurwitz families and groups as Galois groups, Communications in Algebra 5 (1977), 17

Abstract. In [1], a filtration by ramification groups and its logarithmic version are defined on the absolute Galois group of a complete discrete valuation field without assuming that the residue field is perfect. In this paper, we study the graded pieces of these filtrations and show that they are abelian except ...

Language: English ...

We verify a special case of a conjecture of G. Carlsson that describes the $\\l$-adic $K$-theory of a field $F$ of characteristic prime to $\\l$ in terms of the representation theory of the absolute Galois group $G_F$. This conjecture is known to hold in two cases; in this article we examine the second case, in which the field in ...

ON THE ACTION OF THE ABSOLUTE GALOIS GROUP ON DESSINS ERNESTO GIRONDO AND GABINO GONZ�ALEZ-DIEZ Abstract We show-04964 #12;2 ernesto girondo and gabino gonz�alez-diez d'enfants), the action being defined by (Df ) = Df. Schneps, `Dessins d'enfants on the Riemann sphere', pages 47�77 in [5]. Ernesto Girondo Gabino Gonz�alez-Diez

The goal of this paper is to give an explicit description of the triangulated categories of Tate and Artin-Tate motives with finite coefficients Z/m over a field K containing a primitive m-root of unity as the derived categories of exact categories of filtered modules over the absolute Galois group of K with certain restrictions on the ...

Jul 13, 2005... since it is isomorphic to the Galois group of the extension field. ... control of the numerical computations involved in the process. ...

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal ...

For a smooth and geometrically irreducible variety X over a field k , the quotient of the absolute Galois group G_{k(X)} by the commutator subgroup of G_{bar k(X)} projects onto G_k . We investigate the sections of this projection. We show that such sections correspond to ``infinite divisions'' of the elementary obstruction of ...

as Galois groups, Communications in Algebra 5 (1977), 17�82. [Fr78] M. Fried, Galois groups and Complex

We make some observations relating the theory of finite-dimensional differential algebraic groups (the # 0 -groups of [?]) to the Galois theory of linear differential equations. Given a differential field (K, #), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) # 0 ...

We investigate the relations in Galois groups of maximal p-extensions of fields, the structure of their natural filtrations, and their relationship with the Bloch-Kato conjecture proved by Rost and Voevodsky with Weibel's patch. Our main focus is on the third degree, but we provide examples for all degrees.

. For example, the Galois lattice in Figure 1 points out that the three plants ELON (Elodea nuttallii), ELOE (Elodea ernstae) and ELOC (Elodea canadensis) are grouped in the same concept �at the bottom

FORMS OF HOPF ALGEBRAS AND GALOIS THEORY BODO PAREIGIS The theory of Hopf algebras is closely connected with various ap- plications, in particular to algebraic and formal groups. Although the first occurence of Hopf algebras was in algebraic

... Galois over Y with Galois group G, one can view X also as a G-torsor over Y. ... For an algebraic curve the field of moduli is not in general a field of ...

and groups as Galois groups, Communications in Algebra 5 (1977), 17�82. [FrV ]Michael D. Fried and Helmut V

of Function Fields and Hurwitz Families and; Groups as Galois Groups, Communications in Algebra 5 (1977), 17

The notion of stable cohomology of algebraic varieties and, based on it, the analogous concept for finite and profinite groups are introduced. It is proved that the ordinary and stable cohomology coincide for the Galois group of the algebraic closure of a function field with an algebraically closed constant field of characteristic ...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct ...

The purpose of this article is to describe certain results and conjectures concerning the structure of Galois cohomology groups and Selmer groups, especially for abelian varieties. These results are analogues of a classical theorem of Iwasawa. We formulate a very general version of the Weak Leopoldt Conjecture. One consequence of ...

Differential Galois theory, like the more familiar Galois theory of polynomial equations on which it is modeled, aims to understand solving differential equations by exploiting the symmetry group of the field generated by a complete set of solutions to a given equation. The subject was invented in the late nineteenth century, and by ...

The Picard group Martin Bright 14 April 2008 1 Why algebraic geometry? Why should a number theorist of characteristic zero. In particular, in this course we will use the fact that the Picard groups of X over �Q set X(Q) and the Picard group Pic(X�Q) have Galois actions, and we can use ...

The Milnor conjecture has been a driving force in the theory of quadratic forms over fields, guiding the development of the theory of cohomological invariants, ushering in the theory of motivic cohomology, and touching on questions ranging from sums of squares to the structure of absolute Galois groups. Here, we survey some recent work ...

Let F be a field, let G be its absolute Galois group, and let R(G, k) be the representation ring of G over a suitable field k. In this preprint we construct a ring homomorphism from the mod 2 Milnor K-theory k_*(F) to the graded ring gr R(G, k) associated to Grothendieck's \\gamma-filtration. We study this map in particular cases, as ...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 9.2 PPV-extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 9.3 Galois groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 9.4 PPV-Rings and Torsors. A -extension K of k is a Parameterized Picard-Vessiot extension of k (or, more compactly, a ...

Let K a finite extension of Q(sub p), K(sub infinity)/K an extension with Galois group G isomorphic Z(sub p sup r), and X the Galois group of the maximal abelian p-extension of K(sub infinity). The conjugation action of G on X gives rise to a Lambda-modul...

The fractional Galois ideal of [Victor P. Snaith, Stark's conjecture and new Stickelberger phenomena, Canad. J. Math. 58 (2) (2006) 419--448] is a conjectural improvement on the higher Stickelberger ideals defined at negative integers, and is expected to provide non-trivial annihilators for higher K-groups of rings of integers of number fields. In this ...

Let A be an H-Galois extension of B. If M is a Hopf bimodule then HH.(A,M), the Hochschild homology of A with coefficients in M, is a right comodule over the coalgebra C:=H/[H,H]. Given an injective left C-comodule V, we denote the cotensor product of M and V by N. Our aim is to investigate the relationship between the cotensor product of HH.(A,M) and V, on the one hand, and ...

We define the notion of a generic Galois extension with group G over a field F. Let R be a communtative ring of the form F[x(1),..., x(n)](1/s) and let S be a Galois extension of R with group G. Then S/R is generic for G over F if the following holds. Assume K/L is a Galois extension of fields ...

fields and Hurwitz families and groups as Galois groups, Communications in Algebra 5 (1977), 17�82. [Fr

Mathematics is a creative process, and unfortunately, that process is often hidden from students of the discipline. This is certainly the case in the area of mathematics commonly referred to as abstract algebra. Current pedagogy conceals from the student many of the great ideas generated by significant problems in the history of the discipline. In his famous paper "Memoirs on the Conditions for ...

.F. Singer, Algebraic relations among solutions of linear differential equations: Fano's theorem, Am. J. Math that the Galois group does not just depend algebraically on the coefficients of the differential equation solutions of this latter equation to finding solutions of scalar linear differential equations L(y) = 0

, Thomson (Brooks-Cole), (1997), ISBN 0030105595 Reference: Artin-Milgram Galois Theory, Dover (paper $7) (ISBN 0486623424) Garling, Galois Theory, Cambridge Univ. Press (paper $20) (ISBN 0 Algebra) and MATH U575 (Group Theory) or permission of the instructor. Note: only U371 is listed

GALOIS COVERS AND THE HILBERT-GRUNWALD PROPERTY PIERRE D`EBES AND NOUR GHAZI Abstract. Our main, good reduction. 1All profinite group homomorphisms are tacitly assumed to be continuous. 1 #12;2 PIERRE D`EBES be guaranteed to satisfy condition (HGr-spec). #12;4 PIERRE D`EBES AND NOUR GHAZI of part I (�5). Another practical

is algebraically closed. A linear differential equation over K, in vector form, is y = Ay where y is a n � 1 column(�), a finite-dimensional differential algebraic subgroup of G, is Zariski-dense in G. The analogue of a linear be algebraically closed, we can define the notion of a differential Galois extension L of K for the equation

We prove the "divisible case" of the Milnor-Bloch-Kato conjecture (which is the first step of Voevodsky's unfinished proof of this conjecture for arbitrary prime l) in a rather clear and elementary way. Assuming this conjecture, we construct a 6-term exact sequence of Galois cohomology with cyclotomic coefficients for any finite extension of fields whose ...

The purpose of this article is to describe certain results and conjectures concerning the structure of Galois cohomology groups and Selmer groups, especially for abelian varieties. These results are analogues of a classical theorem of Iwasawa. We formulate a very general version of the Weak Leopoldt Conjecture. One consequence of this ...

permutation group." Communications in Algebra 21 (9), 3259-3275 (1993) N.Boston and S.V.Ullom "Representations

Differential (and difference) Galois theorist, algorithmic analyst, and computer algebraist, and professor at North Carolina State University. Available here: books and papers, some in PDF, PostScript, or .dvi versions; course notes for Computational Mathematics for the Life and Management Sciences; and a link to the Symbolic Systems Group (research and ...

This paper contains a proof of the theorem announced in Soviet Math. Dokl. 18 (1977). 535-539 (MR 56 #318). Bibliography: 7 titles.

(1960's): ___ ___ i i (1960's): ___ ___ i i. (Grothendieck, 1960's) For all but finitely many (aa) p the inertia group Ip acts

Abstract. Let k be an algebraic number field. Let ? be a root of a polynomial f ? k[x] which is solvable by radicals. Let L be the splitting field of ? over k. Let n be a natural number divisible by the discriminant of the maximal abelian subextension of L, aswellastheexponentofG(L/k), the Galois group of L over k. We show that an optimal nested radical ...

'ebouche sur un algorithme de calcul du groupe de Galois d'un polynome et de l'id'eal des relations entre ses .) Lorsque l'id'eal de toutes les relations entre les racines de f est connu, le groupe de Galois et le corps construction d'une base de Gr�obner de cet id'eal (voir aussi [23]) ; il consiste `a ...

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(?) of a two-dimensional modular Galois representation ?. We start with the p-adic Galois representation ?₀ of a ...

Galois problem for a finite group G over k amounts to showing that HG(C)(k) = (for some inertia a field extension K/k are the elements of X(K) lying above x. This construction has a global variant over category with a cleavage is equivalent to giving a pseudo- functor. 1.1.1.1 Definition Let p : X C

is equipped with a Gal( #22; Q p =Q p ) action, and a natural inclusion BHT ,! BDi (depending only on the choice =Q p ) action, and show that there is a continuous, C p linear, Galois equivariant embedding BHT ,! B.7). The ring BHT = #8; i2Z C p (i) is absolutely (E; GK ) regular. (Here (i) denotes Tate twist.) Proof. When E

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we study the relation between gradings and Galois coverings. This theoretical tool gives information ...

... Algorithm for Detection and Location of Stuck-at Type Errors in Trees of Galois ... outputs of four-bit Galois linear modules arranged in a tree formation ...

This book review of Galois Theory by Harold Edwards provides a nice survey of Galois's mathematics and how it was perceived by his contemporaries.

GENERIC PICARD-VESSIOT EXTENSIONS FOR NON-CONNECTED GROUPS LOURDES JUAN AND ARNE LEDET Abstract in terms of the first Galois cohomology H1 (K, G) and use it to construct Picard-Vessiot extensions which a linear group G over C, are there a differential field K with field of constants C and a Picard-Vessiot ex

of linear difference equations where the Galois groups are linear differential groups. These groups measure the differential dependence among solutions of linear difference equations. We will show how this theory can difference equations. Solving Linear Differential Equations Marius van der Put Dept. of Math., ...

Introduction The aim of this contribution is to show the possibilities for solving ordinary differential equations with algorithmic methods using Sophus Lie's ideas and computer means. Our material is related especially to Lie's work on transformations and differential equations---essential ideas are already contained in his first paper on transformation groups [5]---and to ...

Through translations of original documents, this article attempts to sift some of the facts of Galois's life from the embroidery of mathematical folklore.

Rings � Structure of Artinian Rings � The X-Topic #12;General Orientation Syllabus Fields and Galois Theory Constructions Galois Theory Assignment Existence of roots Theorem If f(x) = anxn + � � � + a1x + a0 K[x Fields and Galois Theory Ruler and Compass Constructions Galois Theory Assignment To prove ...

In this very short essay we shall describe a 'spectral' point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal ...

numbers of quaternion octic CM-fields are always even. Here, quaternion octic fields, or simply, quaternion fields are number fields whose Galois groups are isomorphic to the quaternion group of order 8. Later, the first author [9] determined all quaternion CM-fields with class number two: there is exactly

(k) of special linear groups. Keywords : Galois cohomology, linear algebraic groups. MSC : 11E72 explicites pour SL 1(A) 16 4.1 Algebres cycliques A est une k-algebre centrale simple. On sait alors que la suite exacte

This site from Northern Illinois University provides online notes for students using the Abstract Algebra textbook (which is also available online). The materials cover the topics of integers, functions, groups, polynomials, communicative rings, fields, structure of groups, Galois theory and unique factorization. Indexes of definitions ...

as supernatural numbers. Let G be the Galois group over F of the field generated over F by all roots of unity in F the Kolyvagin recursion. 3. UNIVERSAL CONSTRUCTIONS 3.1. The free abelian group A . For each supernatural number� r , and G. For each supernatural number s dividing r, let A (s) be the subgroup of A generated

products of prime numbers as supernatural numbers. Let G be the Galois group over F of the #12;eld generated the Kolyvagin recursion. 3. Universal constructions 3.1. The free abelian group A. For each supernatural number Z=Z ! F #2; r , and #27; 2 G. For each supernatural number s dividing r, let A(s) be the subgroup

as supernatural numbers. Let G be the Galois group over F of the field generated over F by all roots of unity in F. Universal constructions 3.1. The free abelian group A. For each supernatural number s put 1 s Z := s|s 1 s Z) = (b) for all a, b 1 r Z/Z, injective homomorphisms : 1 r Z/Z F� r , and G. For each supernatural

... Title : Absolute Determination of Elastic Constants and Stresses from Ultrasonic Group Velocity Data,. Corporate Author : ...

instead of many hours : T48; T36; T25; T44; T38; T40; T41, T33; T29, T19; T24; T13. For example+). _______________________________________________ |[T;_H1]|_____________6_A8;_=_T49______________ | | 162T|50T47T44T38T40T35T30T27T31T43T26T)2 | T50 | || 306; 24|T50T47|T46 | | T3(;6T33;)48;2|T38 | ||| 2; 12; 16T44||T38

algebraic groups and solvability of linear differential equations by quadratures, k-quadratures, generalized, solution of algebraic and linear differential equations. - Topological obstructions to representability function is an elementary function? - When solutions of a linear differential equation can be represented

Taguchi Introduction. This is a written version of my talk under the same title at the Conference. 1 #12; 2 YUICHIRO TAGUCHI of one of these fields. In this paper, however is the orinary #12; 4 YUICHIRO TAGUCHI fundamental group of the n-fold branched cyclic

On a result of Soul�e Romyar Sharifi Spring 2000 Let GS denote the Galois group of the maximal. Soul�e proved the statement of Theorem 1 for all odd primes p and r any positive integer using Chern then dx() = 0 by definition, and dx() = ((-1)r-1 - 1)x inside U(r - 1). If r is odd then we must consider

In this paper, we consider those elliptic curves defined over a quasi-local field with all finite Galois cohomology finite. The main result is the extension, with preservation of nondegeneracy of �afarevi?-Ogg pairing for curves of the given class, to the components of the paired groups corresponding to the characteristic of the residue ...

Taylor, and Andrew Wiles. A broad range of experts on motives, automorphic forms, and Galois collaborations were cited by several visitors as important stimuli to their research. Andrew Wiles, for example, M. Shashahani, and A. Wiles, as well as numerous study sessions organized by M. Kakde on Thursday

* *oration #12; Let G be the Galois group of the linear homogeneous differential equation i d] for a linear differential equation* *. Let 1(z);: :;: m (z) be a fundamental system of solutions of a linear) hold in the case of even t. Then the linear homogeneous differential equation (4)belongs

X(k) n AlbX(k). The 2-cocycles � : n AlbX(k) induced by these sections assemble to a continuous 2 Y be the normalization of X in k(X)( f). Since the pullback map Pic X Pic Y multiplies degree by 2, the middle vertical map in the commutative diagram (Pic X) deg --- Z --- H1 (Qp, Pic0 X) (Pic Y ) deg

by these sections assemble to a continuous 2-cocycle � T(AlbX(k)) that describes the class of in H2 cont(, T). Consider the commutative diagram (Pic X) deg --- Z --- H1 (Qp, Pic0 X) (Pic Y ) deg --- Z --- H1 (Qp, Pic0 Y ) coming from the exact sequence of -modules 0 Pic0 X(Qp) Pic X Z 1 and the similar one

X(k). The 2-cocycles � : n AlbX(k) induced by these sections assemble to a continuous 2-cocycle � : T be the normalization of X in Qp(X)( f). Consider the commutative diagram (Pic X) deg --- Z --- H1 (Qp, Pic0 X) (Pic Y ) deg --- Z --- H1 (Qp, Pic0 Y ) coming from the exact sequence of -modules 0 Pic0 X(Qp) Pic X

This paper introduces two new Burnside rings for a finite group $G$, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of $G$-sets, and of Galois morphisms of $G$-sets, respectively. The well known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, ...

Let f(x) = {x^5} + p{x^3} + q{x^2} + rx + s be an irreducible polynomial of degree 5 with rational coefficients. An explicit resolvent sextic is constructed which has a rational root if and only if f(x) is solvable by radicals (i.e., when its Galois group is contained in the Frobenius group {F_{20}} of order 20 in the symmetric ...

Uniform distribution of Galois conjugates and beta-conjugates of a Parry number near the unit of the Galois conjugates and the beta-conjugates of a Parry number are characterized by means of the Erdos function requires the knowledge of the factorization of the Parry polyno- mial of . This one

An algorithm detects and locates stuck-at type errors from the outputs of four-bit Galois linear modules arranged in a tree formation. An example is given describing the procedure in detail.

When $G$ is abelian and $l$ is a prime we show how elements of the relative K-group $K_{0}({\\bf Z}_{l}[G], {\\bf Q}_{l})$ give rise to annihilator/Fitting ideal relations of certain associated ${\\bf Z}[G]$-modules. Examples of this phenomenon are ubiquitous. Particularly, we give examples in which $G$ is the Galois group of an ...

by the elements of the Brauer group Br X. (Note that in our example the Galois group acts trivially on Pic X) - Hom(F, Pic Y ) - H2 (k, F) H2 (Y, F). (1) If Z Y is a torsor under F, then ([Z]) Hom(F, Pic Y �k �k[Z] T Pic Y Pic Z 0. (2) Moreover, up to sign the map T Pic Y coincides with the type of Z

of the Brauer group Br X. (Note that in our example the Galois group acts trivially on Pic X.) For a numerical) - Hom(F, Pic Y ) - H2 (k, F) H2 (Y, F). (1) If Z Y is a torsor under F, then ([Z]) Hom(F, Pic Y k[Z] T Pic Y Pic Z 0. (2) Moreover, up to sign the map T Pic Y coincides with the type of Z Y

as supernatural numbers. Let G be_the_Galois group over F of the field generated over F by all roots of unity abelian group A. For each supernatural number s put 1_Z := [ 1_Z(b) for all a; b 2 1_rZ=Z, injective homomorphisms OE : 1_rZ=Z ! Fxr, and oe 2 G. * *For each supernatural

... Corporate Author : SPERRY RAND CORP ST PAUL MN ... Personal Author(s) : Ellison, James T. ... of Galois logic design is enhanced in various ways. ...

This collection of pdf files use the PascGalois software for guided explorations in the context of Number Theory course.

This collection of pdf files consists of fully developed lesson plans for using Pascal's Triangle and the PascGalois software for a standard course in Mathematics of Elementary Education.

... Accession Number : ADA106007. Title : Infeld-Hull Factorization, Galois-Picard-Vessiot Theory for Differential Operators,. ...

The report discusses the problems of logic design by means of finite field theory, their interrelationship and some approaches to their solution, with emphasis on logic networks whose function is externally determined. Galois theory is the study of finite...

CONTENTSIntroduction � 1. The group of admissible transformations for measures corresponding to diffusion processes � 2. The absolute continuity of distributions of functionals References

a Galois representation ae : Gal( � K=K) ! GL(H 1 )(Z p ): Moreover the Fontaine's comparison theory (see2]) of Fontaine's comparison theory for C 0 . We have a B + (W (k))� monomorphism of filtered Fontaine's comparison theory we define 8ff 2 J, the de Rham counterpart t ff 2 T(H 1 dR (D) \\Theta 1 p

Let D be an F -central division algebra of degree n. We define D to be quasi- crossed product (QCP and L=K is abelian Galois. If L = K, then D is crossed product. Also, D is said to be soluble QCP that if D* contains an irreducible subgroup satisfying a group identity, then D is QCP. In particular, when

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida�s result accounts for congruences in terms of the value of an L-function, and Ribet�s result is related to the behavior of the period that appears there. Wiles� theory leads to a class number formula relating the value of the L-function to the size ...

From abelian group to zero divisor (definitions), and from Artin-Wedderburn theorem to Wedderburn's theorem, this site provides concise explanations of complex concepts in abstract algebra. Provided by Professor John A. Beachy of Northern Illinois University as a companion to two books he has written, it is designed as a handbook for students studying the topic. The site is ...

We construct an example of a torus $T$ over a field $K$ for which the Galois symbol $K(K; T,T)/n K(K; T,T) \\to H^2(K, T[n]\\otimes T[n])$ is not injective for some $n$. Here $K(K; T,T)$ is the Milnor $K$-group attached to $T$ introduced by Somekawa. We show also that the motive $M(T\\times T)$ gives a counterexample to another generalization of the ...

Systematic method for representing multivariate finite Galois field functions can simplify synthesis

Notes on Galois' memoire Sur les conditions de r�esolubilit�e des �equations par radicaux is a corollary of the theorem. We begin with a result from Proposition VII of Galois' memoir. (In the memoir. The next lemma is a reformulation of Galois' Proposition VI in page 429 of the Memoire (which corre- sponds

Multipliers based on new algorithm for Galois-field (GF) arithmetic regular and expandable. Pipeline

. Galois Theory for Schemes. 2008. [5] David S. Dummit and Richard M. Foote. Abstract Algebra. John WileyGALOIS CATEGORIES MELISSA LYNN Abstract. In abstract algebra, we considered finite Galois. Field Extensions, Separable Algebras 12 Acknowledgments 15 References 15 1. Categories We begin

Abstract. The motivation for this paper is to extend the known model theoretic treatment of differential Galois theory to the case of linear difference equations (where the derivative is replaced by an automorphism.) The model theoretic difficulties in this case arise from the fact that the corresponding theory ACFA does not eliminate quantifiers. We therefore study ...

Let H be a Hopf algebra. By definition a modular crossed H-module is a vector space M on which H acts and coacts in a compatible way. To every modular crossed H-module M we associate a cyclic object Z(H,M). The cyclic homology of Z(H,M) extends the usual cyclic homology of the algebra structure of H, and the relative cyclic homology of an H-Galois extension. For a Hopf ...

and embed X in J(X). The Manin-Mumford conjecture states that the set of torsion points Xtors: = X?Jtors is finite. This conjecture was first proved in 1983 by M. Raynaud [9]. It has long been known that the geometry of X imposes strong conditions on the action of Galois on Xtors. An approach to the Manin-Mumford conjecture using Galois representations ...

"Explicit formulas" in number theory express the sum of values of a function at the zeros of an L-series of an algebraic number field as a sum of local terms corresponding to all norms of this field. For the case of Hecke L-series, such formulas were found earlier by the author. In this paper they are derived for Artin-Hecke series corresponding to arbitrary finite-dimensional representations of ...

Frank Firk is the former Chairman of the Department of Physics at Yale University. He is currently a Professor Emeritus, and his website offers access to three of his textbooks. The first, Essential Physics I, is a guide to classical and special relativity, Newtonian dynamics, gravitation, and wave motion. This textbook is intended for first-year college students. Introduction to ...

Let E be a modular elliptic curve over ?, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F_? be the field obtained by adjoining to ? all p-power division points on E. Write G_? for the Galois group of F_? over ?. Assume that the ...

Let E be a modular elliptic curve over [symbol, see text], without complex multiplication; let p be a prime number where E has good ordinary reduction; and let Finfinity be the field obtained by adjoining [symbol, see text] to all p-power division points on E. Write Ginfinity for the Galois group of Finfinity over [symbol, see text]. Assume that the ...

We prove that, under certain additional assumptions, the endomorphism ring of the Jacobian of a curve y{sup l}=f(x) contains a maximal commutative subring isomorphic to the ring of algebraic integers of the lth cyclotomic field. Here l is an odd prime dividing the degree n of the polynomial f and different from the characteristic of the algebraically closed ground field; moreover, n{>=}9. ...

Abstract. For arithmetical schemes X, K. Kato introduced certain complexes C r,s (X) of Gersten-Bloch-Ogus type whose components involve Galois cohomology groups of all the residue fields of X. For specific (r,s), he stated some conjectures on their homology generalizing the fundamental isomorphisms and exact sequences for Brauer ...

Horeau's method furnishes the correct absolute configuration for those sesquiterpene lactones where one methylene group is adjacent to the asymmetric carbon bearing the hydroxyl group. In 6-hydroxylated pseudoguaianolides a high optical yield can be empir...

as a separate type of power. Power derived from power structures and institutions is depicted in middle drawing opinions as basis of quantities of power. Compatibility of opinions is a separate category of power1 A Model of Absolute Autonomy and Power: Toward Group Effects HENRY HEXMOOR Computer Science

This article is a survey of results on the arithmetic of Abelian varieties that have been obtained by cohomological methods. It consists of an Introduction and six sections. In the Introduction the main facts to be proved in the article are stated. They are concentrated around two arithmetical problems: the determination of the rank of an Abelian variety over a number field and the related problem ...

For one-dimensional three-wave parametric instabilities with oppositely directed group velocities for the decay waves in unbounded plasmas, it is known that for uniform coupling amplitude and constant wave-vector mismatch (dsummationk/sub i//dx = const) there cannot be an absolute instability. It is shown that this is an exceptional case, and that in ...

Monitoring Distributed Hard Real-Time Systems. Lee Pike. Alwyn Goodloe. Galois, Inc. National Institute of Aerospace leepike@galois.com. Alwyn. ...

Finite fields (also called Galois Fields) have been studied since their introduction by Evariste Galois in 1832 and the publication of his work in 1846. In the last few decades, finite fields have become important to information theory, coding theory, and...

FORMS OF HOPF ALGEBRAS AND GALOIS THEORY BODO PAREIGIS The theory of Hopf algebras is closely occurence of Hopf algebras was in algebraic topology, they are now found in areas as remote as combinatorics understood. We are interested in a systematic treatment of Hopf algebras with the techniques of forms

... 22Absolute Astronomy, �Isla Perejil.� ... 31Federation of American Scientists Intelligence Resource Group, �Moroccan Islamic Combatant Group ...

Massey and Omura (1981) recently developed a new multiplication algorithm for Galois fields based on

... Descriptors : *MATHEMATICAL LOGIC, *FIELD THEORY(ALGEBRA), MATRICES(MATHEMATICS), FUNCTIONAL ANALYSIS, FLOW CHARTING ...

The publication of Galois' works in the Journal de Liouville (1846) was announced during a debate between academicians Libri and Liouville as early as 1843. Rather than limiting this publication to a study of controversy, we would like to show that it is inscribed in a larger context of the redefinition of algebra, which this debate illuminates. In order to understand the ...

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work ...

The definition of generalized Hamming weights (GHW) for linear codes over Galois rings is discussed. The properties of GHW for Galois ring linear codes are stated. Upper and existence bounds for GHW of Z{sub 4}-linear codes and a lower bound for GHW of the Kerdock code over Z{sub 4} are derived. GHW of some Z{sub 4}-linear codes are determined.

We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on a rational sublattice which coincides with the Galois field GF[p]. The period of the trajectories increases as a function of the lattice size p and the dimension of the K-matrix d. We emphasize the connection of this approach with the one which is based on primitive ...

to the Fontaine-Mazur Conjectures Yuichiro Taguchi Introduction. The finiteness conjectures mentioned in the title-existence of certain mod p Galois representations, Bull. Korean Math. Soc. 40 (2003), 537�544 [19] H. Moon, Y. Taguchi. Taguchi, Refinement of Tate's discriminant bound and non- existence theorems for mod p Galois

The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations ...

In this note, we explore the computational aspects of several problems in differential algebra with concrete applications in dynamics and motion-planning problems in robotics, automatic synthesis of control schemes for nonlinear systems and simulation of physical systems with fixed degrees of freedom. Our primary aim is to study, compute and structurally describe the solution of a system of ...

It has already been shown that the Fe II absolute oscillator strengths (f-values) measured by Warner

The absolute energies of the principal alpha groups of Rh/sup 223/, Rn/ sup 219/, and Po/sup 215/ were measured by magnetic spectrography. The lengths are compared to a standard model, and the field is measured by nuclear resonance. (tr-auth)

choices. Agents in n-power group have n decisions in common. Definition 6: The power distance between two population is a group of agents whose power distance is 0 and all individually have 0 absolute power level have non- zero powers. If the groups A and B have distance 1, it means that the difference between

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Group theoretical methods are a powerful tool both in their applications to mathematics and to physics. The broad goal of this project was to use such methods to develop the implications of group (symmetry) ...

An apparent discrepancy between the results of Peery and Baumert on the mean absolute magnitude at 1.04 $mu$ of irregularly variable carbon stars is resolved. The mean absolute magnitude of this group of stars derived through a statistical analysis of their proper motions and radial velocities is -4.2 + or - 0.7 (m.e.). (AIP)

... the LFDP. Data are collected at each of 40 points designated as sampling points for animal studies. ... point and absolute and relative humidity. There are 40 groups of data files, one for each of ... ...

Mar 1, 2011 ... An absolute polycythemia was also observed in both centrifuged groups. The results suggest that chronic centrifugation acts through some ...

... Beginning on DG7 � DG 26, mean absolute and relative feed consumptions values in the vaccine treated group were significantly reduced compared to the control ...

Mar 1, 2011 ... An absolute polycythemia was also observed in both centrifuged groups. The results suggest that chronic centrifugation acts through some ...

The following risk prediction models (either absolute risk assessment or genetic susceptibility risk prediction models) are grouped by cancer site and whether their methodology and results have been peer-reviewed.

... results for the crown group age (after considerable algebra) are: Either pair of equations can be used ... dating of phylogenetic trees: A brief review of current methods that estimate divergence tim...

Strain Gage Measurement System to Determine Cryogenic Propellant Tank Level ... The two groups determined the absolute radiometric calibration coefficients ...

Mar 1, 2011 ... An absolute polycythemia was also observed in both centrifuged groups. The results suggest that chronic centrifugation acts through some ...

In this article, we give a way of constructing an unramied Galoiscover of a hyperelliptic curve. The geometric Galois-group is an elementary abelian 2-group. The construction does not make use of the embedding of the curve in its Jacobian and it readily displays all subcovers. We show that the cover we construct is isomorphic to the pullback along the ...

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra and its canonical Ore localisation by using ...

We prove the compatibility of local and global Langlands correspondences for GL_n , which was proved up to semisimplification in M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. of Math. Studies 151, Princeton Univ. Press, Princeton-Oxford, 2001. More precisely, for the n -dimensional l -adic representation R_l(Pi) of the Galois ...

The main topic of the paper is the Hilbert-Grunwald property of Galois covers. It is a property that combines Hilbert's irreducibility theorem, the Grunwald problem and inverse Galois theory. We first present the main results of our preceding paper which concerned covers over number fields. Then we show how our method can be used to unify earlier works on ...

of Galois theory. (iv) Prove or disprove the following, carefully stating every result you use. Suppose [6MA 3D50 GALOIS THEORY solutions -- June 2008 Questions 1, 4 and 5 consist of two or three unrelated as required. (b) Prove or disprove the following. Let K L M be fields and let M be algebraic [5] over K

A practical method of constructing Galois fields of characteristic two and simultaneously giving a way of generating large supply of irreducible polynomials was developed. The only problems left by the Galois field structure theorems are those of finding an irreducible polynomial of degree m over the base field and of finding a primitive generator ...

... classification of title, body of abstract and indexing ... [81 Halmos, Paul R., Lectures on Boolean ... MacLane, S. and Birkhoff, G., Algebra The MacMillan ...

We recall familiar general facts (usually known as Galois cohomology), ... F. The only remaining part is to show that the number of elements in the orbit of ...

and P. Roelse, "Efficient mul- tiplier archtectures for Galois fields GF(24n )," IEEE Trans. Computers

This collection of resources is designed to supplement a modern algebra course. They are designed to help students visualize many of the important concepts from a first semester undergraduate abstract algebra course.

Addresses Abel's proof that the general equation of the fifth degree cannot be solved in radicals without using Galois theory, within the historical context.

Eaton (embedded control systems). n Ericsson (DSP). n Credit Suisse and other trading houses (e.g., derivatives pricing). n Galois (Numerous) ...

and algebra coextensions of Galois type, Communications in Algebra 27 (1999), 1347�1367. [10] G. M. Kelly

Abstract Algebra. - Notation: E the set of all environments. - Galois connection : (ME), C) ' Y , (E#, �). 0t. - U, rw approximated by wit, m# ...

... APPENDIX SA. GALOIS FIELD THEORY ..... ... testing techniques for analog circuits. The sequential circuits are defined over a finite field. Thestý ...

Strictamine (4), strictalamine (6), and nor-C-fluorocurarine (8) have been isolated from Rhazya stricta. X-ray structure determination and chemical correlation establish the structures and absolute configurations of 4, 6, and also, by extension, of the Picralima bases, especially with respect to the configurations of the 16-carbomethoxy group and the ...

Neutron diffraction has been used to monitor the absolute stereochemistry of an enzymatic reaction. (-)(2S)malic-3-d acid was prepared by the action of fumarase on fumaric acid in D/sub 2/O. After a large number of cations were screened, it was found that (+)(R)..cap alpha..-phenylethylamine forms the large crystals necessary for a neutron diffraction analysis. The subsequent ...

Contents: Basic properties of influence measures; An influence measure must be absolutely continuous in the past and have an atom at the present; Semi-groups of translations of functions on (0, infinity); Conditions on the influence function equivalent to...

�1969 � Scotland's History from Macbeth to Braveheart � The Battle for Palestine � Women in Politics: The Powerful Children � Creative Digital Photography � Digital Photography for Absolute Beginners, Group 1 � Digital Photography for Beginners, Group 1 � First Time PC � Introduction to Internet Security � ...

All jihadist orthodoxies hold the core animating belief of absolute intolerance for the religious 'other,' that is other religions and faith groups, as well as other Muslims, whether members of other Muslim groups or individual Muslims who dissent from in...

This paper addresses the significance of the general class of diffeomorphisms in the theory of general relativity as opposed to the Poincare group in a special relativistic theory. Using Anderson's concept of an absolute object for a theory, with suitable revisions, it is shown that the general group of local diffeomorphisms ...

Circular Trellis Coded Modulation (CTCM) defines a family of (block) trellis codes which use a unique algebraic constraint, imposed on the start state, to produce a strong tail-biting property without the inefficiency of driving the encoder state to zero by using a sequence of input zeroes. From the beginning of CTCM, elements of the Galois field, GF(pm), have served dual ...

Circular Trellis Coded Modulation (CTCM) defines a family of (block) trellis codes which use a unique algebraic constraint, imposed on the start state, to produce a strong tail-biting property without the inefficiency of driving the encoder state to zero, using a sequence of input zeroes. Previous papers have investigated specific practical results in the case of binary and 4-ary signaling, using ...

Seventy five patients with severely bleeding peptic ulcer were included in a controlled comparative trial to assess the efficacy and safety of endoscopic injection therapy in preventing rebleeding from peptic ulcers that presented at endoscopy with a protruding vessel. Twenty five patients were treated with injection of epinephrine followed by polidocanol, 25 were treated with injection of ...

The structure of the group G(k[t]): Variations on a theme of Soule Benedictus Margaux Abstract. Following Soule's ideas [14] we give a presentation of the abstract group G(k[t]) for any semisimple absolutely almost simple k--group. For G split, Soule [14] has given a presentation of the group G

Yuichiro Taguchi Abstract. A formula is given to describe how the Artin conductor of a * *mod (1987), 179-230. 9. Y. Taguchi, On Artin conductors of mod ` Galois representations, unpublishe* *d manuscript. Graduate School of Mathematics Kyushu University 33 Fukuoka 812-8581, Japan taguchi@math.kyushu-u.ac.jp

Gaggles, Gentzen and Galois: A Proof Theory for Algebraizable Logics Rajeev Gor'e Automated�classical logics like modal logic [Wan94], intuitionistic and intermediate logics [Gor95], and substructural logics to explain the display property [Gor94b] and also to handle Dunn's general setting of tonoids [Gor94a

Any Hopf algebra fibers over an affine variety of the same dimension Christian Kassel Institut de and let H be a Hopf algebra over k � Aljadeff and I constructed an H-Galois extension BH AH whose algebra be a Hopf algebra over k � Aljadeff and I constructed an H-Galois extension BH AH whose algebra

, the com� plexity of this circuitry can also be ignored as c !! k. 3 A Super�Serial Multiplier 3 with c. The serial multiplier core uses mainly function gen� erators and memory elements. It uses onlyA Super�Serial Galois Fields Multiplier for FPGAs and its Application to Public�Key Algorithms

Reed-Solomon (RS) codes have found many applications such as space and mobile communication due to their error correcting capability (ECC) and optimum structure. It is shown that time domain algorithms are the best candidates for designing versatile hardware decoders, but syndrome based algorithms are advantageous for software decoders. The algorithms for decoding RS codes require algebraic ...

Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of the integers modulo a prime characteristic p. They can be used to generate efficient cyclic encoding, for transmitting secrete quantum keys, ...

candidate for a cohomology theory AG which gives rise to the formal group G. Namely, for every finite cell spaces (Y X) to abelian groups. (We recover the absolute cohomology groups An (X) by taking Y = .) (2 of cohomology with coefficients in any abelian group M: one simply replaces Z by M in ...

A novel synthetic path to sequosempervirin A was established by employing a samarium diiodide promoted intramolecular Barbier-type reaction of the lactonic iodide, in which the key structural feature, a spiro[4.5]decane ring system, could be constructed by controlling the stereochemistry of the hydroxyl group at the 8-position. The absolute configuration ...

The effect of helium and oxygen at ambient and 21 atmospheres absolute (ATA) upon feed digestibility and utilization was studied. Three groups of growing male guinea pigs were fed Ried-Briggs diet and subjected to environments of air and helium-oxygen at ...

The Absolute Neutron Activation Analysis (ANAA) technique was used to determine element concentrations of Cl and Na in blood of healthy group (male and female blood donators), select from Blood Banks at Sao Paulo city, to provide information which can help in diagnosis of patients. This study permitted to perform a discussion about the advantages and ...

We introduce �braidability� as a new symmetry for infinite sequences of noncommutative random variables related to representations of the braid group {mathbb{B}_{infty}} . It provides an extension of exchangeability which is tied to the symmetric group {mathbb{S}_{infty}} . Our key result is that braidability implies spreadability and thus conditional ...

Computer simulations of the free-electron laser have been carried out using a two-and-one-half dimensional fully electromagnetic relativistic particle code. It has been found that waves propagating obliquely with respect to the electron beam are always unstable with appreciable growth rates and, therefore, mode competition is an important consideration in the design of free-electron lasers. ...

This report discusses six issues that affect the measurement of disparities in health between groups in a population: Selecting a reference point from which to measure disparity; Measuring disparity in absolute or in relative terms; Measuring in terms of ...

The spontaneous symmetry breaking pattern for SU(n) and 0(10) is discussed. It is based on the exact treatment of the absolute minimum of the Higgs potential as a function of scalar fields belonging to the fundamental and adjoint representations of SU(n),...

This work involves several different groups using different techniques to build DTMs from the same starting data in order to assess various absolute and relative measures of the quality of LROC NAC derived terrain data.

A group of tables is presented listing accurate theoretical line positions and absolute emission intensities for individual multiplet-vibration-rotation transitions in the ground state of nitric oxide. The data covers both intramultiplet and intermultiple...

... To illustrate the method, we determine the phase velocities in a very lossy, 50-mm-thick, glass/epoxy specimen in the 0.3-1.2-MHz region. (Author). ...

In a previous communication (JACS v87 p1958, 1965), an empirical rule was proposed that '(-)-methyl alkyl sulfoxides which do not contain other strongly perturbing groups have negative Cotton effects centered at the strong absorption band near 200 millimi...

We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions {\\tilde{\\chi }}^{(n)}'s of the susceptibility of the Ising model for n <= 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator ...

Three groups of Clark's nutcrackers (Nucifraga columbiana) were trained to find a goal location defined by an array of 4 landmarks that varied in goal--landmark distance. The arrays for each group differed in the distance of the closest landmark and contained goal--landmark distances that were common across groups, allowing for the ...

Standard Galois Lattices are effective tools for data analysis and knowledge discovery. They allow structuring data sets, by extracting concepts and rules to deduce concepts from other concepts. They focus on binary data arrays, called contexts. Several algorithms were proposed to generate concepts or concept lattices on a data context. However, the mining of large databases ...