Lattices in PU(n,1) that are not profinitely rigid

2018/08/22 by Stover, Matthew
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1808.07344

Abstract

Using conjugation of Shimura varieties, we produce nonisomorphic, cocompact, torsion-free lattices in PU(n,1) with isomorphic profinite completions for all n ≥ 2. This disproves a conjecture of D. Kazhdan and gives the first examples nonisomorphic lattices in a semisimple Lie group of real rank one with isomorphic profinite completions, answering two questions of A. Reid.

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