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Algebraic Groups And Number Theory

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Algebraic Groups And Number Theory

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Author : Vladimir Platonov
language : en
Publisher: Academic Press
Release Date : 1993-12-07

Algebraic Groups And Number Theory written by Vladimir Platonov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-07 with Mathematics categories.

This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

Algebraic Groups And Number Theory

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Author : Vladimir Platonov
language : en
Publisher: Academic Press
Release Date : 1993-10-19

Pure And Applied Mathematics

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Author : Vladimir Petrovich Platonov
language : en
Publisher:
Release Date : 1994

Pure And Applied Mathematics written by Vladimir Petrovich Platonov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebraic number theory categories.

Representations Of Algebraic Groups

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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-01-01

Representations Of Algebraic Groups written by Jens Carsten Jantzen 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 2003-01-01 with Mathematics categories.

Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. Here, the author describes important basic notions: induction functors, cohomology,quotients, Frobenius kernels, and reduction mod $p$, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, andSchubert schemes and line bundles on them. For this revised edition the author added nearly 150 pages of new material describing some later developments, among them Schur algebras, Lusztig's conjecture and Kazhdan-Lusztig polynomials, tilting modules, and representations of quantum groups. He also made major revisions to parts of the old text. Jantzen's book continues to be the ultimate source of information on representations of algebraic groups in finite characteristics. It is suitable forgraduate students and research mathematicians interested in algebraic groups and their representations.

Algebraic Groups And Number Theory

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Author : Vladimir Petrovich Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07

Algebraic Groups And Number Theory written by Vladimir Petrovich Platonov 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 2023-09-07 with Mathematics categories.

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Algebraic Groups And Number Theory Volume 1

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Author : Vladimir Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07

Algebraic Groups And Number Theory Volume 1 written by Vladimir Platonov 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 2023-09-07 with Mathematics categories.

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

Linear Algebraic Groups

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Author : Tonny Albert Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Linear Algebraic Groups written by Tonny Albert 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 1998 with Mathematics categories.

"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly styleâ¦ [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literatureâ¦appear for the first time in a text." âMathematical Reviews(Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index." âZentralblatt Math(Review of the Second Edition)

Adeles And Algebraic Groups

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

Adeles And Algebraic Groups written by A. Weil 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.

This volume contains the original lecture notes presented by A. Weil in which the concept of adeles was first introduced, in conjunction with various aspects of C.L. Siegel’s work on quadratic forms. These notes have been supplemented by an extended bibliography, and by Takashi Ono’s brief survey of subsequent research. Serving as an introduction to the subject, these notes may also provide stimulation for further research.

Algebraic Groups And Their Representations

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Author : R.W. Carter
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-31

Algebraic Groups And Their Representations written by R.W. Carter 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 1998-08-31 with Mathematics categories.

This volume contains articles by 20 leading workers in the field of algebraic groups and related finite groups. Articles on representation theory are written by Andersen on tilting modules, Carter on canonical bases, Cline, Parshall and Scott on endomorphism algebras, James and Kleshchev on the symmetric group, Littelmann on the path model, Lusztig on homology bases, McNinch on semisimplicity in prime characteristic, Robinson on block theory, Scott on Lusztig's character formula, and Tanisaki on highest weight modules. Articles on subgroup structure are written by Seitz and Brundan on double cosets, Liebeck on exceptional groups, Saxl on subgroups containing special elements, and Guralnick on applications of subgroup structure. Steinberg gives a new, short proof of the isomorphism and isogeny theorems for reductive groups. Aschbacher discusses the classification of quasithin groups and Borovik the classification of groups of finite Morley rank. Audience: The book contains accounts of many recent advances and will interest research workers and students in the theory of algebraic groups and related areas of mathematics.

Linear Algebraic Groups

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Author : T.A. Springer
language : en
Publisher: Birkhäuser
Release Date : 2014-01-29

Linear Algebraic Groups written by T.A. Springer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-29 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.

Algebraic Groups And Number Theory

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