Equivariant geometry and the cohomology of the moduli space of curves

2010/06/11 by Dan Edidin, Edidin, Dan · 3 citations
Mathematics · #14D23 #14H10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1006.2364

openalex publication_date 2010/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes
• Getzler-Kapranov complexes and moduli stacks of curves
• The Evaluation Space of Logarithmic Stable Maps

Related

• Cohomology of moduli spaces
• The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points
• Relative étale slices and cohomology of moduli spaces
• Equivariant Elliptic Cohomology and Mapping Stacks I
• Moduli stack of stable curves from a stratified homotopy viewpoint