Algebraic Groups And Arithmetic
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Algebraic Groups and Arithmetic
Major advances have been made in recent decades in algebraic groups and arithmetic. The School of Mathematics of the Tata Institute of Fundamental Research, under the leadership of Professor M. S. Raghunathan, has been a significant contributor to this progress. This collection of papers grew out of a conference held in honor of Professor Raghunathan's sixtieth birthday. The volume contains original papers contributed by leading experts. Topics covered include group-theoretic aspects, Diophantine approximation, modular forms, representation theory, interactions with topology and geometry, and dynamics on homogeneous spaces. Particularly noteworthy are two expository articles on Professor Raghunathan's work by the late Armand Borel and Gopal Prasad. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.
Linear Algebraic Groups
Author: Armand Borel
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over non-algebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs.
Algebraic Groups and Number Theory
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.