Formal GAGA for good moduli spaces

TL;DR

This paper proves a version of formal GAGA for good moduli space morphisms, showing they behave similarly to proper morphisms under certain conditions, which enhances understanding of their geometric properties.

Contribution

It establishes formal GAGA results for good moduli spaces under the 'enough vector bundles' assumption, applicable to quotient stacks.

Findings

Formal GAGA holds for good moduli space morphisms with enough vector bundles.

Supports the view that good moduli spaces behave like proper morphisms.

Applicable to quotient stacks, broadening the scope of formal GAGA results.

Abstract

We prove formal GAGA for good moduli space morphisms under an assumption of "enough vector bundles" (which holds for instance for quotient stacks). This supports the philosophy that though they are non-separated, good moduli space morphisms largely behave like proper morphisms.