Lattices in $\mathrm{PU}(n,1)$ that are not profinitely rigid

Matthew Stover

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arXiv · 1808.07344

Lattices in $\mathrm{PU}(n,1)$ that are not profinitely rigid

Matthew Stover

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Abstract

Using conjugation of Shimura varieties, we produce nonisomorphic, cocompact, torsion-free lattices in $\mathrm{PU}(n,1)$ with isomorphic profinite completions for all $n \ge 2$. 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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Matthew Stover. 2018-08-22. Lattices in $\mathrm{PU}(n,1)$ that are not profinitely rigid. https://arxiv.org/abs/1808.07344

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