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Equivariant geometry and the cohomology of the moduli space of curves (1006.2364v2)
Published 11 Jun 2010 in math.AG
Abstract: In this expository article we give a categorical definition of the integral cohomology ring of a stack. We show that for quotient stacks the categorical cohomology may be identified with equivariant cohomology. Via this identification we show that for Deligne-Mumford quotient stacks this cohomology is rationally isomorphic to the rational cohomology of the coarse moduli space. The theory is presented with a focus on the stacks of smooth and stable curves.