Arithmetic equivalence for function fields, the Goss zeta function and a generalisation

Cornelissen, Gunther and Kontogeorgis, Aristides and van der Zalm, Lotte

Abstract

We consider three examples of families of curves over a non-archimedean valued field which admit a non-trivial group action. These equivariant deformation spaces can be described by algebraic parameters (in the equation of the curve), or by rigid-analytic parameters (in the Schottky group of the curve). We study the relation between these parameters as rigid-analytic self-maps of the disk