Jump to ContentJump to Main Navigation
Classification of Pseudo-reductive Groups (AM-191)$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see www.princeton.universitypressscholarship.com/page/privacy-policy).date: 26 September 2018

Generalization of the standard construction

Generalization of the standard construction

Chapter:
9 Generalization of the standard construction
Source:
Classification of Pseudo-reductive Groups (AM-191)
Author(s):

Brian Conrad

Gopal Prasad

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691167923.003.0009

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 is reduced, the first step is to remove that restriction. Thus, in the non-reduced case the focus is on the longest (equivalently, divisible) roots when defining the root field of G. For absolutely pseudo-simple k-groups of minimal type with a non-reduced root system over ks the condition that the root field coincides with the ground field is a reasonable one to impose for the purpose of a structure theorem. The chapter proves a rigidity property of generalized standard presentations involving the notion of “pseudo-isogeny.” It concludes with a detailed discussion of the structure theorem.

Keywords:   generalized standard, pseudo-reductive group, root field, root system, pseudo-simple k-group, minimal type, structure theorem, rigidity property, generalized standard presentation, pseudo-isogeny

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.