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Descent in Buildings (AM-190)$
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Descent in Buildings (AM-190)

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

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Residually Pseudo-Split Buildings

Residually Pseudo-Split Buildings

Chapter:
(p.287) Chapter Thirty Three Residually Pseudo-Split Buildings
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/9780691166902.003.0033

This chapter presents results about a residually pseudo-split Bruhat-Tits building Ξ‎L. It begins with a case for some quadratic space of type E⁶, E₇, and E₈ in order to identify an unramified extension such that the residue field is a pseudo-splitting field. It then considers a wild quaternion or octonion division algebra and the existence of an unramified quadratic extension L/K such that L is a splitting field of the quaternion division algebra. It also discusses the properties of an unramified extension L/K and shows that every exceptional Bruhat-Tits building is the fixed point building of a strictly semi-linear descent group of a residually pseudo-split building.

Keywords:   quadratic space, Bruhat-Tits building, residue, pseudo-splitting field, octonion division algebra, unramified quadratic extension, quaternion division algebra, fixed point building, descent group, residually pseudo-split building

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