Algebraic Groups And Class Fields
DOWNLOAD
Download Algebraic Groups And Class Fields PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Groups And Class Fields book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Algebraic Groups And Class Fields
DOWNLOAD
Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Groups And Class Fields written by Jean-Pierre Serre 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.
Translation of the French Edition
Algebraic Groups And Class Fields
DOWNLOAD
Author : Jean-Pierre Serre
language : en
Publisher:
Release Date : 1988
Algebraic Groups And Class Fields written by Jean-Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Galois Cohomology And Class Field Theory
DOWNLOAD
Author : David Harari
language : en
Publisher: Springer Nature
Release Date : 2020-06-24
Galois Cohomology And Class Field Theory written by David Harari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-24 with Mathematics categories.
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
Algebraic Groups
DOWNLOAD
Author : J. S. Milne
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-21
Algebraic Groups written by J. S. Milne 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 2017-09-21 with Mathematics categories.
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Unipotent And Nilpotent Classes In Simple Algebraic Groups And Lie Algebras
DOWNLOAD
Author : Martin W. Liebeck
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-01-25
Unipotent And Nilpotent Classes In Simple Algebraic Groups And Lie Algebras written by Martin W. Liebeck 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 2012-01-25 with Mathematics categories.
This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
Local Fields
DOWNLOAD
Author : Jean-Pierre Serre
language : en
Publisher: Springer
Release Date : 1995-07-27
Local Fields written by Jean-Pierre Serre and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-27 with Mathematics categories.
The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Conjugacy Classes In Semisimple Algebraic Groups
DOWNLOAD
Author : James E. Humphreys
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Conjugacy Classes In Semisimple Algebraic Groups written by James E. Humphreys 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 1995 with Education categories.
Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.
Class Field Theory
DOWNLOAD
Author : Georges Gras
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Class Field Theory written by Georges Gras 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 2013-11-11 with Mathematics categories.
Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.
Algebra In Action A Course In Groups Rings And Fields
DOWNLOAD
Author : Shahriar Shahriar
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-16
Algebra In Action A Course In Groups Rings And Fields written by Shahriar Shahriar 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 2017-08-16 with Mathematics categories.
This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Linear Algebraic Groups
DOWNLOAD
Author : T.A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-13
Linear Algebraic Groups written by T.A. Springer 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 2008-11-13 with Mathematics categories.
The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.