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arXiv · 1802.08559

Profinite commensurability of S-arithmetic groups

Holger Kammeyer
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Abstract

Given an S-arithmetic group, we ask how much information on the ambient algebraic group, number field of definition, and set of places S is encoded in the commensurability class of the profinite completion. As a first step, we show that the profinite commensurability class of a higher rank S-arithmetic group determines the number field up to arithmetical equivalence and the places in S above unramified primes. We include applications to profiniteness questions of group invariants.

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Holger Kammeyer. 2018-02-23. Profinite commensurability of S-arithmetic groups. https://arxiv.org/abs/1802.08559

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