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Profinite commensurability of $S$-arithmetic groups

Volume 197 / 2021

Holger Kammeyer Acta Arithmetica 197 (2021), 311-330 MSC: Primary 20G30; Secondary 20G25, 11F75. DOI: 10.4064/aa200401-23-7 Published online: 11 November 2020

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.

Authors

  • Holger KammeyerInstitute for Algebra and Geometry
    Karlsruhe Institute of Technology
    Englerstr. 2 (Mathebau 20.30)
    76131 Karlsruhe, Germany
    e-mail

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