Jump to ContentJump to Main Navigation
Descent in Buildings (AM-190)$
Users without a subscription are not able to see the full content.

Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

Print publication date: 2015

Print ISBN-13: 9780691166902

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691166902.001.0001

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 http://www.universitypressscholarship.com/page/privacy-policy).date: 20 July 2018

Quadrangles of Type F4

Quadrangles of Type F4

Chapter:
(p.129) Chapter Seventeen Quadrangles of Type F4
Source:
Descent in Buildings (AM-190)
Author(s):

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691166902.003.0017

This chapter deals with the case that the building at infinity Λ‎ of the Bruhat-Tits building Ξ‎ is a Moufang quadrangle of type F₄. It begins with the hypothesis stating that Λ‎ = (K, L, q) is a quadratic space of type F₄, K is complete with respect to a discrete valuation ν‎ and F is closed with respect to ν‎, Λ‎ is the Moufang quadrangle corresponding to a root group sequence, and R₀ and R₁ as the two residues of Ξ‎. The chapter also considers the theorem supposing that Λ‎ is of type F₄ and that R₀ and R₁ are not both indifferent, and claims that both cases really occur. Finally, it presents the proposition that R₀ and R₁ are both indifferent if and only if q is totally wild.

Keywords:   residue, Bruhat-Tits building, Moufang quadrangle, quadratic space, discrete valuation, root group sequence

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.