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Galois Module Structure
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Book Synopsis Galois Module Structure by : Victor Percy Snaith
Download or read book Galois Module Structure written by Victor Percy Snaith and published by American Mathematical Soc.. This book was released on 1994 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions.
Book Synopsis Multiplicative Galois Module Structure by : A. Weiss
Download or read book Multiplicative Galois Module Structure written by A. Weiss and published by American Mathematical Soc.. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the result of a short course on the Galois structure of S -units that was given at The Fields Institute in the autumn of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behaviour of Artin L -functions at s = 0. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of S -units can be described. This is intended for graduate students and research mathematicians, specifically algebraic number theorists.
Book Synopsis Multiplicative Galois Module Structure by : Alfred Weiss
Download or read book Multiplicative Galois Module Structure written by Alfred Weiss and published by American Mathematical Soc.. This book was released on 1996 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the result of a short course on the Galois structure of S -units that was given at The Fields Institute in the autumn of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behaviour of Artin L -functions at s = 0. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of S -units can be described. This is intended for graduate students and research mathematicians, specifically algebraic number theorists.
Book Synopsis Galois Module Structure of Algebraic Integers by : Albrecht Fröhlich
Download or read book Galois Module Structure of Algebraic Integers written by Albrecht Fröhlich and published by Springer. This book was released on 1983 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Module Structure of Algebraic Integers by : A. Fröhlich
Download or read book Galois Module Structure of Algebraic Integers written by A. Fröhlich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.
Book Synopsis Hopf Algebras and Galois Module Theory by : Lindsay N. Childs
Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Book Synopsis Galois Module Structure in Wild Extensions of the Rationale Function Field by : Raymond Miller
Download or read book Galois Module Structure in Wild Extensions of the Rationale Function Field written by Raymond Miller and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Class Group Relations and Galois Module Structure by : Bart De Smit
Download or read book Class Group Relations and Galois Module Structure written by Bart De Smit and published by . This book was released on 1993 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic K-Groups as Galois Modules by : Victor P. Snaith
Download or read book Algebraic K-Groups as Galois Modules written by Victor P. Snaith and published by Birkhäuser. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume began as the last part of a one-term graduate course given at the Fields Institute for Research in the Mathematical Sciences in the Autumn of 1993. The course was one of four associated with the 1993-94 Fields Institute programme, which I helped to organise, entitled "Artin L-functions". Published as [132]' the final chapter of the course introduced a manner in which to construct class-group valued invariants from Galois actions on the algebraic K-groups, in dimensions two and three, of number rings. These invariants were inspired by the analogous Chin burg invariants of [34], which correspond to dimensions zero and one. The classical Chinburg invariants measure the Galois structure of classical objects such as units in rings of algebraic integers. However, at the "Galois Module Structure" workshop in February 1994, discussions about my invariant (0,1 (L/ K, 3) in the notation of Chapter 5) after my lecture revealed that a number of other higher-dimensional co homological and motivic invariants of a similar nature were beginning to surface in the work of several authors. Encouraged by this trend and convinced that K-theory is the archetypical motivic cohomology theory, I gratefully took the opportunity of collaboration on computing and generalizing these K-theoretic invariants. These generalizations took several forms - local and global, for example - as I followed part of number theory and the prevalent trends in the "Galois Module Structure" arithmetic geometry.
Book Synopsis Galois Module Structure of the Integers of E - Extensions by : Martin John Taylor
Download or read book Galois Module Structure of the Integers of E - Extensions written by Martin John Taylor and published by . This book was released on 1977 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Module Structure for Square Classes of Units in Klein 4-group Extensions by : Frank A. Chemotti
Download or read book Galois Module Structure for Square Classes of Units in Klein 4-group Extensions written by Frank A. Chemotti and published by . This book was released on 2005 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory by : Lindsay Childs
Download or read book Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory written by Lindsay Childs and published by American Mathematical Soc.. This book was released on 2000 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree p and p2; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.
Book Synopsis Galois Module Structure in Wild Extensions of the Rational Function Field by : Raymond Miller
Download or read book Galois Module Structure in Wild Extensions of the Rational Function Field written by Raymond Miller and published by . This book was released on 1997 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Module Structure of Galois Cohomology by : Andrew Schultz
Download or read book Galois Module Structure of Galois Cohomology written by Andrew Schultz and published by . This book was released on 2007 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cohomology groups associated to the absolute Galois group of a field E encode a great deal of information about E, with the groups Hm(GE, mu p) being of classical interest. These groups are linked to the reduced Milnor K-groups KmE/pK mE = kmE by the Bloch-Kato conjecture. Using this conjecture when E/F is a Galois extension of fields with Gal(E/F) ≃ Z/pnZ for some odd prime p, and additionally assuming xi p ∈ E, we study the groups H m(GE, mup) as modules over the group ring Fp [Gal(E/F)]. When E/F embeds in an extension E'/F with Gal(E'/F) ≃ Z/pn+1 Z , we are able to give a highly stratified decomposition of Hm(GE, mup). This allows us to give a decomposition of the cohomology groups of a p-adic extension of fields. In general we are able to give a coarse decomposition of Hm(GE, mu p), showing that many indecomposable types do not appear in Hm(GE, mup). With an additional assumption about the norm map Nnn-1 : kmEn → k mEn-1, we strengthen this coarse decomposition to a highly stratified one.
Book Synopsis The Galois Module Structure of the Integers in Wildly Ramified Extensions by : Gove Griffith Elder
Download or read book The Galois Module Structure of the Integers in Wildly Ramified Extensions written by Gove Griffith Elder and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Module Structure of Lubin-Tate Modules by : Sebastian Tomaskovic-Moore
Download or read book Galois Module Structure of Lubin-Tate Modules written by Sebastian Tomaskovic-Moore and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additive Galois modules, the ring of integers OL of L is studied as a module for the group ring OKG, where G is the Galois group of L/K. When K is a p-adic field, we also find a structure of OKG module when we replace OL with the group of points in OL of a Lubin-Tate formal group defined over K. For this new Galois module we find an analogue of the normal basis theorem. When K is a proper unramified extension of Qp , we show that some eigenspaces for the Teichmüller character are not free. We also adapt certain cases of E. Noether's result on normal integral bases for tame extensions. Finally, for wild extensions we define a version of Leopoldt's associated order and demonstrate in a specific case that it is strictly larger than the integral group ring.
Book Synopsis An Equal-distribution Result for Galois Module Structure by : Kurt Christopher Foster
Download or read book An Equal-distribution Result for Galois Module Structure written by Kurt Christopher Foster and published by . This book was released on 1987 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
