Geodesic
Definable equivalence relations and zeta functions of groups (with an appendix by Raf Cluckers)
Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2467-2537

Voir la notice de l'article provenant de la source EMS Press

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 alternative proof, using cell decomposition, of the rationality (for fixed p) of these formal zeta functions that extends to the subanalytic context.
DOI : 10.4171/jems/817
Classification : 03-XX, 11-XX, 20-XX
Keywords: Elimination of imaginaries, invariant extensions of types, cell decompositions, rational zeta functions, subgroup zeta functions, representation zeta functions 
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     title = {Definable equivalence relations and zeta functions of groups (with an appendix by {Raf} {Cluckers)}},
     journal = {Journal of the European Mathematical Society},
     pages = {2467--2537},
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Ehud Hrushovski; Ben Martin; Silvain Rideau. Definable equivalence relations and zeta functions of groups (with an appendix by Raf Cluckers). Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2467-2537. doi: 10.4171/jems/817

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