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Introduction

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0001
Subject:
Mathematics, Numerical Analysis

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 ... More


Automorphisms, isomorphisms, and Tits classification

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0006
Subject:
Mathematics, Numerical Analysis

This chapter considers automorphisms, isomorphisms, and Tits classification. It begins by establishing a version of the Isomorphism Theorem for pseudo-split pseudo-reductive groups, along with a ... More


Preliminary notions

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0002
Subject:
Mathematics, Numerical Analysis

This chapter considers some preliminary notions, starting with standard pseudo-reductive groups, Levi subgroups, and root systems. It reviews the “standard construction” of pseudo-reductive k-groups ... More


Field-theoretic and linear-algebraic invariants

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0003
Subject:
Mathematics, Numerical Analysis

This chapter deals with field-theoretic and linear-algebraic invariants. It first presents a construction of non-standard pseudo-split absolutely pseudosimple k-groups with root system A1 over any ... More


Central extensions and groups locally of minimal type

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0004
Subject:
Mathematics, Numerical Analysis

This chapter deals with central extensions and groups locally of minimal type. It begins with a discussion of the general lemma on the behavior of the scheme-theoretic center with respect to the ... More


Generalization of the standard construction

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0009
Subject:
Mathematics, Numerical Analysis

This chapter deals with “generalized standard” pseudo-reductive group over a field k. Because the notion of root field has only been defined for absolutely pseudo-simple G whose root system over ks ... More


Classification of Pseudo-reductive Groups (AM-191)

Brian Conrad and Gopal Prasad

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.001.0001
Subject:
Mathematics, Numerical Analysis

This book goes further than the exploration of the general structure of pseudo-reductive groups to study the classification over an arbitrary field. An Isomorphism Theorem proved here determines the ... More


Universal smooth <i>k</i>-tame central extension

Brian Conrad and Gopal Prasad

in Classification of Pseudo-reductive Groups (AM-191)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.003.0005
Subject:
Mathematics, Numerical Analysis

This chapter describes the construction of canonical central extensions that are analogues for perfect smooth connected affine k-groups of the simply connected central cover of a connected semisimple ... More


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