Profinite commensurability of S-arithmetic groups
Group Theory
2020-07-24 v2 Number Theory
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.
Cite
@article{arxiv.1802.08559,
title = {Profinite commensurability of S-arithmetic groups},
author = {Holger Kammeyer},
journal= {arXiv preprint arXiv:1802.08559},
year = {2020}
}
Comments
Final version to appear in Acta Arith., 18 pages