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Classification of Pseudo-reductive Groups (AM-191)$
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Brian Conrad and Gopal Prasad

Print publication date: 2015

Print ISBN-13: 9780691167923

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691167923.001.0001

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(p.1) 1 Introduction
Classification of Pseudo-reductive Groups (AM-191)

Brian Conrad

Gopal Prasad

Princeton University Press

This book deals with the classification of pseudo-reductive groups. Using new techniques and constructions, it addresses a number of questions; for example, whether there are versions of the Isomorphism and Isogeny Theorems for pseudosplit pseudo-reductive groups and of the Existence Theorem for pseudosplit pseudo-simple groups; whether the automorphism functor of a pseudo-semisimple group is representable; or whether there is a Tits-style classification in the pseudo-semisimple case recovering the version due to Tits in the semisimple case. This introduction discusses the special challenges of characteristic 2 as well as root systems, exotic groups and degenerate quadratic forms, and tame central extensions. It also reviews generalized standard groups, minimal type and general structure theorem, and Galois-twisted forms and Tits classification.

Keywords:   pseudo-reductive group, Isomorphism Theorem, Isogeny Theorem, automorphism functor, pseudo-semisimple group, Tits-style classification, characteristic 2, root system, degenerate quadratic form, generalized standard group

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