Journal article

Definable equivalence relations and zeta functions of groups

Abstract:

We prove that the theory of the $p$-adics ${\mathbb Q}_p$ admits elimination of imaginaries provided we add a sort for ${\rm GL}_n({\mathbb Q}_p)/{\rm GL}_n({\mathbb Z}_p)$ for each $n$. We also prove that the elimination of imaginaries is uniform in $p$. Using $p$-adic and motivic integration, we deduce the uniform rationality of certain formal zeta functions arising from definable equivalence relations. This also yields analogous results for definable equivalence relations over local fields...

Publication status:
Not published
Peer review status:
Not peer reviewed

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Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Funding agency for:
Cluckers, R
Grant:
ANR-11-LABX-0007-01
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Funding agency for:
Rideau, S
Grant:
ANR-09-BLAN-0047
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Funding agency for:
Hrushovski, E
Cluckers, R
Grant:
291111/MODAG
ANR-11-LABX-0007-01
Journal:
arXiv
Publication date:
2015-08-21
Keywords:
Pubs id:
pubs:648791
UUID:
uuid:40384ddd-d973-49c2-8d9a-8898007b8695
Local pid:
pubs:648791
Source identifiers:
648791
Deposit date:
2017-01-13