Algebraic Groups And Number Theory PDF Download
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Author | : Vladimir Platonov |
Publisher | : Academic Press |
Total Pages | : 629 |
Release | : 1993-12-07 |
Genre | : Mathematics |
ISBN | : 0080874592 |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
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 | : Vladimir Petrovich Platonov |
Publisher | : |
Total Pages | : 614 |
Release | : 1994 |
Genre | : Algebraic number theory |
ISBN | : 9780125581806 |
Download Pure and Applied Mathematics Book in PDF, ePub and Kindle
Author | : Vladimir Platonov |
Publisher | : Academic Press |
Total Pages | : 614 |
Release | : 1993-11-02 |
Genre | : Mathematics |
ISBN | : 9780125581806 |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
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 | : Vladimir Platonov |
Publisher | : Cambridge University Press |
Total Pages | : 380 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 1009380656 |
Download Algebraic Groups and Number Theory: Volume 1 Book in PDF, ePub and Kindle
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.
Author | : J. S. Milne |
Publisher | : Cambridge University Press |
Total Pages | : 665 |
Release | : 2017-09-21 |
Genre | : Mathematics |
ISBN | : 1107167485 |
Download Algebraic Groups Book in PDF, ePub and Kindle
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author | : T.A. Springer |
Publisher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2010-10-12 |
Genre | : Mathematics |
ISBN | : 0817648402 |
Download Linear Algebraic Groups Book in PDF, ePub and Kindle
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 | : A. Weil |
Publisher | : Springer Science & Business Media |
Total Pages | : 137 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468491563 |
Download Adeles and Algebraic Groups Book in PDF, ePub and Kindle
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 | : Meinolf Geck |
Publisher | : Oxford University Press |
Total Pages | : 321 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 019967616X |
Download An Introduction to Algebraic Geometry and Algebraic Groups Book in PDF, ePub and Kindle
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 | : Arkadij L. Onishchik |
Publisher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 364274334X |
Download Lie Groups and Algebraic Groups Book in PDF, ePub and Kindle
This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Author | : Jens Carsten Jantzen |
Publisher | : American Mathematical Soc. |
Total Pages | : 594 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082184377X |
Download Representations of Algebraic Groups Book in PDF, ePub and Kindle
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.