TL;DR
This paper introduces a notion of stability for Artin stacks, constructs coarse moduli spaces for stable points, and applies these concepts to coherent cohomology, advancing the understanding of algebraic stacks.
Contribution
It defines stability on arbitrary Artin stacks and constructs coarse moduli spaces for their stable points, providing new tools for their analysis.
Findings
Construction of coarse moduli spaces for stable points
Introduction of stability notion on Artin stacks
Application to coherent cohomology
Abstract
This paper is largely concerned with constructing coarse moduli spaces for Artin stacks. The main purpose of this paper is to introduce the notion of stability on an arbitrary Artin stack and construct a coarse moduli space for the open substack of stable points. Also, we present an application to coherent cohomology of Artin stacks.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds