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

الأصل · EN

We compute the étale cohomology groups Hⁱ(X,Gₘ) 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 H²(X, Gₘ) does not depend on X but only on the underlying orbicurve and on the generic stabilizer.