Multiplicative Galois Module Structure

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Multiplicative Galois Module Structure

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Author : Alfred Weiss
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Multiplicative Galois Module Structure written by Alfred Weiss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

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.

Multiplicative Galois Module Structure

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Author : A. Weiss
language : en
Publisher: American Mathematical Soc.
Release Date :

Multiplicative Galois Module Structure written by A. Weiss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

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.

Multiplicative Galois Module Structure

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Author : A. Weiss
language : en
Publisher:
Release Date : 2012

Multiplicative Galois Module Structure written by A. Weiss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Galois modules (Algebra) categories.

Galois Module Structure

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Author : Victor Percy Snaith
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Galois Module Structure written by Victor Percy Snaith and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

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.

Algebraic K Groups As Galois Modules

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Author : Victor P. Snaith
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Algebraic K Groups As Galois Modules written by Victor P. Snaith and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Galois Representations In Arithmetic Algebraic Geometry

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Author : A. J. Scholl
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-26

Galois Representations In Arithmetic Algebraic Geometry written by A. J. Scholl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-26 with Mathematics categories.

Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

Elementary And Analytic Theory Of Algebraic Numbers

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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Elementary And Analytic Theory Of Algebraic Numbers written by Wladyslaw Narkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

The aim of this book is to present an exposition of the theory of alge braic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numeri cal computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis. Thus the author has tried to reconcile the two approaches, presenting a self-contained exposition of the classical standpoint in the first four chapters, and then turning to local methods. In the first chapter we present the necessary tools from the theory of Dedekind domains and valuation theory, including the structure of finitely generated modules over Dedekind domains. In Chapters 2, 3 and 4 the clas sical theory of algebraic numbers is developed. Chapter 5 contains the fun damental notions of the theory of p-adic fields, and Chapter 6 brings their applications to the study of algebraic number fields. We include here Shafare vich's proof of the Kronecker-Weber theorem, and also the main properties of adeles and ideles.

Class Group Relations And Galois Module Structure

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Author : Bart De Smit
language : en
Publisher:
Release Date : 1993

Class Group Relations And Galois Module Structure written by Bart De Smit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Algebra And Number Theory

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Author : Gerhard Frey
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20

Algebra And Number Theory written by Gerhard Frey and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.

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.

The Second Chinburg Conjecture For Quaternion Fields

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Author : Jeff Hooper
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

The Second Chinburg Conjecture For Quaternion Fields written by Jeff Hooper and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.