Root stack valuative criterion for good moduli spaces

TL;DR

This paper establishes a valuative criterion for root stacks related to good moduli spaces and gerbes, with applications in torsor extensions, rational points, and geometric structures under mild residue characteristic assumptions.

Contribution

It introduces a root stack valuative criterion for good moduli space maps and gerbes, expanding tools for algebraic stack analysis under mild conditions.

Findings

Provides a criterion applicable to reductive group gerbes

Applications to parahoric extension for torsors

Insights into rational points and fibration geometry

Abstract

We prove a root stack valuative criterion for good moduli space maps and for gerbes for reductive groups under some mild assumptions on the residue characteristic. We give several applications to parahoric extension for torsors, rational points on stacks, gerbes and homogeneous spaces, and the geometry of fibrations.