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Galois Module Structure Of Algebraic Integers
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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 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. Frohlich
Download or read book Galois Module Structure of Algebraic Integers written by A. Frohlich and published by . This book was released on 1983-03-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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 . This book was released on 2002-03-01 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 1994-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first published graduate course on the Chinburg conjectures, and this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems.
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 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 Elementary and Analytic Theory of Algebraic Numbers by : Wladyslaw Narkiewicz
Download or read book Elementary and Analytic Theory of Algebraic Numbers written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Book Synopsis Algebraic Number Fields by : Albrecht Fröhlich
Download or read book Algebraic Number Fields written by Albrecht Fröhlich and published by . This book was released on 1977 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Second Chinburg Conjecture for Quaternion Fields by : Jeff Hooper
Download or read book The Second Chinburg Conjecture for Quaternion Fields written by Jeff Hooper and published by American Mathematical Soc.. This book was released on 2000 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Chinburg Conjecture relates the Galois module structure of rings of integers in number fields to the values of the Artin root number on the symplectic representations of the Galois group. This book establishes the Second Chinburg Conjecture for various quaternion fields.
Book Synopsis Algebra and Number Theory by : Gerhard Frey
Download or read book Algebra and Number Theory written by Gerhard Frey and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis The Trace Map and Galois Module Structure of Rings of Integers for Absolutely Abelian Number Fields by : Henri Louis Alistair Johnston
Download or read book The Trace Map and Galois Module Structure of Rings of Integers for Absolutely Abelian Number Fields written by Henri Louis Alistair Johnston and published by . This book was released on 2007 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebra written by I.B.S. Passi and published by Birkhäuser. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Indian National. Science Academy has planned to bring out monographs on special topics with the aim of providing acce~sible surveys/reviews of topics of current research in various fields. Prof. S.K. Malik, FNA, Editor of Publications INSA asked me in October 1997 to edit a volume on algebra in this series. I invited a number of algebraists, several of them working in group rings, and it is with great satisfaction and sincere thanks to the authors that I present here in Algebra: Some Recent Advances the sixteen contributions received in response to my invitations. I.B.S. Passi On Abelian Difference Sets K. r Arasu* and Surinder K. Sehgal 1. Introduction We review some existence and nonexistence results - new and old - on abelian difference sets. Recent surveys on difference sets can be found in Arasu (1990), Jungnickel (1992a, b), Pott (1995), Jungnickel and Schmidt (1997), and Davis and Jedwab (1996). Standard references for difference sets are Baumert (1971), Beth et al. (1998), and Lander (1983). This article presents a flavour of the subject, by discussing some selected topics. Difference sets are very important in combinatorial design theory and in commu nication engineering while designing sequences with good correlation properties. Our extended bibliography covers a wide variety of papers written in the area of difference sets and related topics.
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.
