Cohomological amplitude for constructible sheaves on moduli spaces of curves
Abstract
We give bounds for the cohomology of constructible sheaves on the moduli stacks Mg,n over the complex field. This enables us recover Harer's bound for the virtual cohomological dimension of the associated mapping class groups as well the theorem of Diaz on complete subvarieties of Mg. We also obtain such bounds for any open subset of the Deligne-Mumford compactification of Mg,n that is a union of strata. Our proof yields a template for obtaining similar bounds for the cohomological dimension for quasicoherent sheaves on Mg,n.
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