Addendum: \'Etale d\'evissage, descent and pushouts of stacks

TL;DR

This paper develops new techniques using Nisnevich coverings and Hilbert stacks to analyze algebraic stacks, leading to advances in approximation and derived category generation.

Contribution

It introduces novel étale dévissage methods for non-representable coverings and applies them to algebraic stack approximation and derived category theory.

Findings

Proves étale dévissage results for non-representable coverings

Provides applications to noetherian approximation of stacks

Establishes compact generation of derived categories

Abstract

Using Nisnevich coverings and a Hilbert stack of stacky points, we prove \'etale d\'evissage results for non-representable \'etale and quasi-finite flat coverings. We give applications to absolute noetherian approximation of algebraic stacks and compact generation of derived categories.