Definable equivalence relations and zeta functions of groups (with an appendix by Raf Cluckers)
Definable equivalence relations and zeta functions of groups (with an appendix by Raf Cluckers)
We prove that the theory of the p -adics {\mathbb Q}_p admits elimination of imaginaries provided we add a sort for {\mathrm GL}_n({\mathbb Q}_p)/{\mathrm 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 …