Generalised Poincar\'e series and embedded resolution of curves

Abstract

The purpose of this paper is to extend the notions of generalised Poincar\'e series and divisorial generalised Poincar\'e series (of motivic nature) introduced by Campillo, Delgado and Gusein-Zade for complex curve singularities to curves defined over perfect fields, as well as to express them in terms of an embedded resolution of curves.