Strong cycles and intersection products on good moduli spaces

TL;DR

This paper proposes conjectures linking the Chow ring of smooth Artin stacks to the Chow groups of their potentially singular good moduli spaces, focusing on intersection products derived from strong cycles.

Contribution

It introduces conjectures about the structure of Chow rings and intersection products on good moduli spaces related to smooth Artin stacks, a novel theoretical framework.

Findings

Conjectures established relating Chow rings and Chow groups.

Proposed intersection product on a subgroup of Chow groups.

Framework connecting smooth stacks to singular moduli spaces.

Abstract

We introduce conjectures relating the Chow ring of a smooth Artin stack $\mathcal{X}$ to the Chow groups of its possibly singular good moduli space $X$. In particular, we conjecture the existence of an intersection product on a subgroup of the full Chow group $A^*(X)$ coming from strong cycles on $\mathcal{X}$.