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Fall and Winter 2016 Local-to-global rigidity of Bruhat–Tits buildings
Mikael De La Salle, Romain Tessera
Illinois J. Math. 60(3-4): 641-654 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067284


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 $d\geq4$. We show that the $1$-skeleton of an affine Bruhat–Tits building of type $\widetilde{A}_{d-1}$ is local-to-global rigid if and only if the underlying field has characteristic $0$. For example, the Bruhat–Tits building of $\mathrm{SL}(d,\mathbf{F}_{p}(\!(t)\!))$ is not local-to-global rigid, while the Bruhat–Tits building of $\mathrm{SL}(d,\mathbf{Q}_{p})$ is local-to-global rigid.


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Mikael De La Salle. Romain Tessera. "Local-to-global rigidity of Bruhat–Tits buildings." Illinois J. Math. 60 (3-4) 641 - 654, Fall and Winter 2016.


Received: 9 December 2015; Revised: 22 February 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 1376.20033
MathSciNet: MR3707639
Digital Object Identifier: 10.1215/ijm/1506067284

Primary: 20E42 , 20F65

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign


Vol.60 • No. 3-4 • Fall and Winter 2016
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