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Pseudo-Split Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0028
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces a class of Moufang spherical buildings known as pseudo-split buildings and considers the notion of the field of definition of a spherical building satisfying the Moufang ... More


Forms of Residually Pseudo-Split Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0034
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with forms of residually pseudo-split buildings. The proof rests on the fact that in every case, there is a Galois action of Γ‎ := GalL/K on Δ‎L whose fixed point building is ... More


Residually Pseudo-Split Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0033
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

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 ... More


Descent in Buildings (AM-190)

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

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This book begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. It then puts forward an algebraic solution into a geometric context by developing a ... More


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