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Constructions when Φ‎ has a double bond

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/9780691167923.003.0008
Subject:
Mathematics, Numerical Analysis

This chapter describes constructions when Φ‎ has a double bond. In particular, it considers a construction that goes beyond SO(q)'s and provides the right generalization of the basic exotic ... More


Constructions with regular degenerate quadratic forms

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/9780691167923.003.0007
Subject:
Mathematics, Numerical Analysis

This chapter uses degenerate quadratic forms and quadrics in Severi–Brauer variety to give a geometric description of all non-standard absolutely pseudo-simple k-groups G of minimal type with root ... 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


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


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