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Definable equivalence relations and zeta functions of groups (with an appendix by Raf Cluckers)

Abstract:

We prove that the theory of the p-adics Qp admits elimination of imaginaries provided we add a sort for GLn(Qp)/GLn(Zp) 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 of positive characteristic. The appendix contains an alter...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/JEMS/817

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-2761-6513
Publisher:
European Mathematical Society Publishing House Publisher's website
Journal:
Journal of the European Mathematical Society Journal website
Volume:
20
Issue:
10
Pages:
2467-2537
Publication date:
2018-07-18
Acceptance date:
2017-06-25
DOI:
EISSN:
1435-9863
ISSN:
1435-9855

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