Computing the equivariant Euler characteristic of Zariski and étale sheaves on curves

Abstract

We prove an equivariant Grothendieck-Ogg-Shafarevich formula. This formula may be viewed as an étale analogue of well-known formulas for Zariski sheaves generalizing the classical Chevalley-Weil formula. We give a new approach to those formulas (first proved by Ellingsrud/Lønsted, Nakajima, Kani and Ksir) which can also be applied in the étale case.