Rational points of rigid-analytic sets: a Pila-Wilkie type theorem

Abstract

We establish a rigid-analytic analog of the Pila-Wilkie counting theorem, giving sub-polynomial upper bounds for the number of rational points in the transcendental part of a ${\mathbb{Q}}_p$-analytic set, and the number of rational functions in a ${\mathbb{F}}_q((t))$-analytic set. For $\mathbb{Z}[[t]]$-analytic sets we prove such bounds uniformly for the specialization to every non-archimedean local field.

References in corpus (1)

• Point counting for foliations over number fields