Algebraic Groups And Number Theory
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Author |
: Vladimir Platonov |
Publisher |
: Academic Press |
Total Pages |
: 629 |
Release |
: 1993-12-07 |
ISBN-10 |
: 9780080874593 |
ISBN-13 |
: 0080874592 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Algebraic Groups and Number Theory by : Vladimir Platonov
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.
Author |
: J. S. Milne |
Publisher |
: Cambridge University Press |
Total Pages |
: 665 |
Release |
: 2017-09-21 |
ISBN-10 |
: 9781107167483 |
ISBN-13 |
: 1107167485 |
Rating |
: 4/5 (83 Downloads) |
Synopsis Algebraic Groups by : J. S. Milne
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author |
: A. Weil |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 137 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468491562 |
ISBN-13 |
: 1468491563 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Adeles and Algebraic Groups by : A. Weil
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.
Author |
: T.A. Springer |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 347 |
Release |
: 2010-10-12 |
ISBN-10 |
: 9780817648404 |
ISBN-13 |
: 0817648402 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Linear Algebraic Groups by : T.A. Springer
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.
Author |
: Meinolf Geck |
Publisher |
: Oxford University Press |
Total Pages |
: 321 |
Release |
: 2013-03-14 |
ISBN-10 |
: 9780199676163 |
ISBN-13 |
: 019967616X |
Rating |
: 4/5 (63 Downloads) |
Synopsis An Introduction to Algebraic Geometry and Algebraic Groups by : Meinolf Geck
An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Author |
: Armand Borel |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 301 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461209416 |
ISBN-13 |
: 1461209412 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Linear Algebraic Groups by : Armand Borel
This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.
Author |
: Jens Carsten Jantzen |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 594 |
Release |
: 2003 |
ISBN-10 |
: 9780821843772 |
ISBN-13 |
: 082184377X |
Rating |
: 4/5 (72 Downloads) |
Synopsis Representations of Algebraic Groups by : Jens Carsten Jantzen
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author |
: James E. Humphreys |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 259 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468494433 |
ISBN-13 |
: 1468494430 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Linear Algebraic Groups by : James E. Humphreys
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.
Author |
: Toshiaki Shoji |
Publisher |
: American Mathematical Society(RI) |
Total Pages |
: 514 |
Release |
: 2004 |
ISBN-10 |
: UOM:39015061859339 |
ISBN-13 |
: |
Rating |
: 4/5 (39 Downloads) |
Synopsis Representation Theory of Algebraic Groups and Quantum Groups by : Toshiaki Shoji
A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.
Author |
: Pavel I. Etingof |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 240 |
Release |
: 2011 |
ISBN-10 |
: 9780821853511 |
ISBN-13 |
: 0821853511 |
Rating |
: 4/5 (11 Downloads) |
Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.