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Non-archimedean geometry, motivic integration and rational points

The aim is to further investigate non-archimedean geometry, motivic integration and rational points via hensel minimality, existential positive motivic integration and quasi-analytic functions. Hensel minimality provides a geometric framework for non-archimedean geometry. Within this framework, we can study quasi-analytic functions, similar to o-minimality. This then leads to the counting and bounding of rational points. Motivic integration will be studied, with extra focus on quantifiers and positivity This leads to new descent results, for example, for the largest non-trivial poles, when descending from a larger field to a smaller one.

Date:15 Sep 2021 →  Today
Keywords:Non-archimedean geometry, Hensel minimality, Motivic integration
Disciplines:Algebraic geometry , Measure and integration, Number theory, Mathematical logic and foundations
Project type:PhD project