Archive | 2019
Lattices in (,1) that are not profinitely rigid
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.