Class Group Relations And Galois Module Structure

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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.

Galois Module Structure Of Algebraic Integers

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Author : A. Fröhlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Galois Module Structure Of Algebraic Integers written by A. Fröhlich 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 2012-12-06 with Mathematics categories.

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.

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.

Galois Module Structure Of Algebraic Integers

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Author : Albrecht Fröhlich
language : en
Publisher: Springer
Release Date : 1983

Galois Module Structure Of Algebraic Integers written by Albrecht Fröhlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

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.

Geometry And Dynamics Of Groups And Spaces

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Author : Mikhail Kapranov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-05

Geometry And Dynamics Of Groups And Spaces written by Mikhail Kapranov 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 2008-03-05 with Mathematics categories.

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Galois Module Structure

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Author : Victor Percy Snaith
language : en
Publisher: American Mathematical Soc.
Release Date : 1994-01-01

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 1994-01-01 with Mathematics categories.

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.

Group Rings And Class Groups

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Author : K.W. Roggenkamp
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-03-31

Group Rings And Class Groups written by K.W. Roggenkamp 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 1992-03-31 with Mathematics categories.

"The workshops organized by the gesellschaft fur mathematische Forschung in cooperation with the Deutsche Mathematiker-Vereingung (German Mathematics Society) are intended to help, in particular, students and younger mathematicians, to obtain an introduction to fields of current research. Through the means of these well-organized seminars, scientists and younger mathematicians, to obtain an introduction to fields of current research. Through the means of these well-organized seminars, scientists form other fields can also be introduced to new mathematical ideas. The publication of these workshops in the series DMV SEMINAR will make all the material available to an even wider audience." --Publisher.

Journ Es Arithm Tiques 1980

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Author : J. V. Armitage
language : en
Publisher: Cambridge University Press
Release Date : 1982-09-16

Journ Es Arithm Tiques 1980 written by J. V. Armitage 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 1982-09-16 with Mathematics categories.

Covers all branches of number theory.

Orders And Their Applications

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Author : Irving Reiner
language : en
Publisher: Springer
Release Date : 2006-11-14

Orders And Their Applications written by Irving Reiner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

With contributions by numerous experts