Hensel minimaliteit, motivische integratie en rationale punten

We study non-Archimedean geometry, motivic integration and rational points via Hensel minimality, cell decomposition and existential positive motivic integration. Hensel minimality provides a simultaneously broad and powerful framework for non-Archimedean geometry. We extend this framework to new classes of structures and apply it to study the counting and bounding of (generalized) rational points. Motivic integration is studied, with extra control on existential quantifiers. This leads to a new descent results for the largest poles of generating series of p-adic point counts, when descending from a larger field to a smaller subfield.