Tempered fundamental group - E.Lepage

Mar 21, 2023  ·   From Paris France  ·   Event ``Arithmetic & Homotopic Galois Theory 2023''

Abstract

The goal of this talk is to review results and applications of the tempered fundamental group in anabelian geometry. The tempered fundamental group of a variety over a non-archimedean field, defined by Y.André, classifies a category of covers which contain finite covers, but also some infinite covers such as the uniformization of Tate curves.
Whereas its profinite completion coincides with the profinite étale fundamental group, the tempered fundamental group has interesting anabelian features even over algebraically closed fields of mixed characteristics.