Title Classification of pseudo-reductive groups / Brian Conrad, Gopal Prasad

Published ©2016 Princeton : Princeton University Press, 2016

Click on the following:
ProQuest Ebook Central

Copies

Description 1 online resource (1 volume) Series Annals of mathematics studies ; number 191 Annals of mathematics studies ; no. 191. Contents Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Motivation; 1.2 Root systems and new results; 1.3 Exotic groups and degenerate quadratic forms; 1.4 Tame central extensions; 1.5 Generalized standard groups; 1.6 Minimal type and general structure theorem; 1.7 Galois-twisted forms and Tits classification; 1.8 Background, notation, and acknowledgments; 2 Preliminary notions; 2.1 Standard groups, Levi subgroups, and root systems; 2.2 The basic exotic construction; 2.3 Minimal type; 3 Field-theoretic and linear-algebraic invariants; 3.1 A non-standard rank-1 construction Summary In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic Analysis "ient homomorphism Cartan k-subgroup Dynkin diagram Isogeny Theorem Isomorphism Theorem Levi subgroup Tits classification Tits-style classification Weil restriction algebraic geometry automorphism functor automorphism scheme automorphism canonical central extensions central "ient central extension characteristic 2 conformal isometry degenerate quadratic form double bond exotic construction field-theoretic invariant generalized exotic group generalized standard group generalized standard presentation generalized standard isomorphism class isomorphism isotropic group k-tame central extension linear isomorphism linear-algebraic invariant maximal torus minimal type non-reduced root system number theory pseudo-isogeny pseudo-reductive group pseudo-semisimple group pseudo-simple group pseudo-simple k-group pseudo-split form pseudo-split quadratic space quadrics rank-1 rank-2 rigidity property root field root system scheme-theoretic center semisimple "ient semisimple k-group structure theorem Bibliography Includes bibliographical references and index Notes In English Print version record Subject Linear algebraic groups. Group theory. Geometry, Algebraic. MATHEMATICS -- Algebra -- Intermediate. MATHEMATICS -- Mathematical Analysis. Geometry, Algebraic Group theory Linear algebraic groups Form Electronic book Author Prasad, Gopal LC no. 2015023803 ISBN 1400874025 9781400874026

  Permalink