\'Etale cohomology of a DM curve-stack with coefficients in G_m
Algebraic Geometry
2014-08-28 v2
Abstract
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.
Cite
@article{arxiv.1008.0538,
title = {\'Etale cohomology of a DM curve-stack with coefficients in G_m},
author = {Flavia Poma},
journal= {arXiv preprint arXiv:1008.0538},
year = {2014}
}
Comments
13 pages, comments welcome