Local-to-global rigidity of bruhat-tits buildings

Mikael De La Salle; Romain Tessera

doi:10.1215/ijm/1506067284

Local-to-global rigidity of bruhat-tits buildings

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Abstract

A vertex-transitive graph X is called local-to-global rigid if there exists R such that every other graph whose balls of radius R are isometric to the balls of radius R in X is covered by X. Let d ≥ 4. We show that the 1-skeleton of an affine Bruhat-Tits building of type Ã_d-1 is local-to-global rigid if and only if the underlying field has characteristic 0. For example, the Bruhat-Tits building of SL(d,F_p((t))) is not local-to-global rigid, while the Bruhat-Tits building of SL(d,Q_p) is local-toglobal rigid.

Original language	English
Pages (from-to)	641-644
Number of pages	4
Journal	Illinois Journal of Mathematics
Volume	60
Issue number	3-4
DOIs	https://doi.org/10.1215/ijm/1506067284
Publication status	Published - 1 Sept 2016
Externally published	Yes

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title = "Local-to-global rigidity of bruhat-tits buildings",

abstract = "A vertex-transitive graph X is called local-to-global rigid if there exists R such that every other graph whose balls of radius R are isometric to the balls of radius R in X is covered by X. Let d ≥ 4. We show that the 1-skeleton of an affine Bruhat-Tits building of type {\~A}d-1 is local-to-global rigid if and only if the underlying field has characteristic 0. For example, the Bruhat-Tits building of SL(d,Fp((t))) is not local-to-global rigid, while the Bruhat-Tits building of SL(d,Qp) is local-toglobal rigid.",

author = "\{De La Salle\}, Mikael and Romain Tessera",

note = "Publisher Copyright: {\textcopyright} 2017 University of Illinois.",

year = "2016",

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doi = "10.1215/ijm/1506067284",

language = "English",

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journal = "Illinois Journal of Mathematics",

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AU - De La Salle, Mikael

AU - Tessera, Romain

PY - 2016/9/1

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N2 - A vertex-transitive graph X is called local-to-global rigid if there exists R such that every other graph whose balls of radius R are isometric to the balls of radius R in X is covered by X. Let d ≥ 4. We show that the 1-skeleton of an affine Bruhat-Tits building of type Ãd-1 is local-to-global rigid if and only if the underlying field has characteristic 0. For example, the Bruhat-Tits building of SL(d,Fp((t))) is not local-to-global rigid, while the Bruhat-Tits building of SL(d,Qp) is local-toglobal rigid.

AB - A vertex-transitive graph X is called local-to-global rigid if there exists R such that every other graph whose balls of radius R are isometric to the balls of radius R in X is covered by X. Let d ≥ 4. We show that the 1-skeleton of an affine Bruhat-Tits building of type Ãd-1 is local-to-global rigid if and only if the underlying field has characteristic 0. For example, the Bruhat-Tits building of SL(d,Fp((t))) is not local-to-global rigid, while the Bruhat-Tits building of SL(d,Qp) is local-toglobal rigid.

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DO - 10.1215/ijm/1506067284

M3 - Article

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VL - 60

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EP - 644

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 3-4

ER -

Local-to-global rigidity of bruhat-tits buildings

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