Algebraic Groups and Number Theory: Volume 1
Algebraic Groups and Number Theory: Volume 1

Author: Vladimir Platonov

Publisher: Cambridge University Press

Published: 2023-08-31

Total Pages: 380

ISBN-13: 1009380656

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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.

Algebraic Groups and Number Theory
Algebraic Groups and Number Theory

Author: Vladimir Platonov

Publisher: Academic Press

Published: 1993-12-07

Total Pages: 629

ISBN-13: 0080874592

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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
Algebraic Groups and Number Theory

Author: Vladimir Petrovich Platonov

Publisher:

Published: 2023

Total Pages: 0

ISBN-13: 9781139017756

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"This is the first volume of a two-volume book that offers an in-depth, and essentially self-contained, treatment of the arithmetic theory of algebraic groups. It is accessible to graduate students and researchers in number theory, algebraic geometry, and related areas"--

Algebraic Groups
Algebraic Groups

Author: J. S. Milne

Publisher: Cambridge University Press

Published: 2017-09-21

Total Pages: 665

ISBN-13: 1107167485

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Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Linear Algebraic Groups
Linear Algebraic Groups

Author: James E. Humphreys

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 259

ISBN-13: 1468494430

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James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

Adeles and Algebraic Groups
Adeles and Algebraic Groups

Author: A. Weil

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 137

ISBN-13: 1468491563

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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. Serving as an introduction to the subject, these notes may also provide stimulation for further research.

Linear Algebraic Groups
Linear Algebraic Groups

Author: T.A. Springer

Publisher: Springer Science & Business Media

Published: 2010-10-12

Total Pages: 347

ISBN-13: 0817648402

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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 Geometry and Number Theory
Algebraic Geometry and Number Theory

Author: victor ginzburg

Publisher: Springer Science & Business Media

Published: 2007-12-31

Total Pages: 656

ISBN-13: 0817645322

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This book represents a collection of invited papers by outstanding mathematicians in algebra, algebraic geometry, and number theory dedicated to Vladimir Drinfeld. Original research articles reflect the range of Drinfeld's work, and his profound contributions to the Langlands program, quantum groups, and mathematical physics are paid particular attention. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.