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# 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: http://dx.doi.org/10.4310/HHA.2005.v7.n3.a6

#### Author

#### 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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

14F20, 14H30, 14L30