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.
General
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