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Adelic superrigidity
and profinitely solitary lattices
Holger Kammeyer and Steffen Kionke |
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Vol. 313 (2021), No. 1, 137–158
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DOI: 10.2140/pjm.2021.313.137
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Abstract |
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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. |
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Keywords
profinite rigidity, arithmeticity, superrigidity
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Mathematical Subject Classification
Primary: 20E18, 22E40
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Milestones
Received: 19 February 2021
Revised: 21 June 2021
Accepted: 22 June 2021
Published: 17 September 2021
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Authors |
| Holger Kammeyer | |
| Mathematisches Institut Heinrich-Heine-Universität Düsseldorf Düsseldorf Germany |
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| Steffen Kionke | |
| FernUniversität in Hagen Hagen Germany |
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