TOWARDS AN INTERSECTION CHOW COHOMOLOGY THEORY FOR GIT QUOTIENTS

Abstract

We study the Fulton-MacPherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces are etale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore natural extensions of GIT quotients. Our main result is that, with ℚ-coefficients, every operational class can be represented by a topologically strong cycle on the corresponding stack. Moreover, this cycle is unique modulo rational equivalence on the stack. Our methods also allow us to prove that if X is the good moduli space of a properly stable, smooth, Artin stack then the natural map Pic(X)ℚ, L ↦ c1(L) is an isomorphism.