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The Quasi-Isomorphism Theorem

Richard Evan Schwartz

in The Plaid Model: (AMS-198)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691181387
eISBN:
9780691188997
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181387.003.0019
Subject:
Mathematics, Educational Mathematics

This chapter proves the Quasi-Isomorphism Theorem modulo two technical lemmas, which will be dealt with in the next two chapters. Section 18.2 introduces the affine transformation TA from 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


Graphic Matroids

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0006
Subject:
Mathematics, Educational Mathematics

This chapter examines graphic matroids in more detail. In particular, it presents several proofs delayed from Chapters 1 and 2, including proofs that a graphic matroid is representable over every ... More


The Orbit Equivalence Theorem

Richard Evan Schwartz

in The Plaid Model: (AMS-198)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691181387
eISBN:
9780691188997
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181387.003.0018
Subject:
Mathematics, Educational Mathematics

This chapter begins Part 4 of the monograph. The goal of this part is to prove the Orbit Equivalence Theorem and the Quasi-Isomorphism Theorem. Theorem 17.1 (Orbit Equivalence) states that there is a ... More


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


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


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