Vol. 313, No. 1, 2021

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Adelic superrigidity and profinitely solitary lattices

Holger Kammeyer and Steffen Kionke

Vol. 313 (2021), No. 1, 137–158
DOI: 10.2140/pjm.2021.313.137
Abstract

By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of or . We prove an adelic version of superrigidity which implies that two such commensurability classes define the same profinite commensurability class if and only if the algebraic groups are adelically isomorphic. We discuss noteworthy consequences on profinite rigidity questions.

Keywords
profinite rigidity, arithmeticity, superrigidity
Mathematical Subject Classification
Primary: 20E18, 22E40
Milestones
Received: 19 February 2021
Revised: 21 June 2021
Accepted: 22 June 2021
Published: 17 September 2021
Authors
Holger Kammeyer
Mathematisches Institut
Heinrich-Heine-Universität Düsseldorf
Düsseldorf
Germany
Steffen Kionke
FernUniversität in Hagen
Hagen
Germany