Étale cohomology of a DM curve-stack with coefficients in G_m

Details Étale cohomology of a DM curve-stack with coefficients in G_m Étale cohomology of a DM curve-stack with coefficients in G_m

2010-08-03

arxiv.org/abs/1008.0538v2

Mathematics

Algebraic Geometry

13 pages, comments welcome

Scientific paper

We compute the \'etale cohomology groups H^i(X,G_m) in several cases, where X is a smooth tame Deligne-Mumford stack of dimension 1 over an algebraically closed field. We have complete results for orbicurves (and, more generally, for twisted nodal curves) and in the case all stabilizers are cyclic; we give some partial results and examples in the general case. In particular we show that if the stabilizers are abelian then H^2(X, G_m) does not depend on X but only on the underlying orbicurve and on the generic stabilizer.

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