Homology, Homotopy and Applications

Volume 7 (2005)

Number 3

Proceedings of a Conference in honour of Victor Snaith

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

Pages: 83 – 98

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n3.a6


Bernhard Köck (School of Mathematics, University of Southampton, United Kingdom)


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.


equivariant Euler characteristic, étale cohomology, Grothendieck-Ogg-Shafarevich formula, conductor, Lefschetz formula, Riemann-Roch formula, Hurwitz formula

2010 Mathematics Subject Classification

14F20, 14H30, 14L30

Published 1 January 2005