Compact approximation and descent for algebraic stacks

Abstract

This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are quasi-finite and flat. This generalizes a result of Lipman--Neeman for schemes and extends a related result known for algebraic spaces. We also study the behavior of generation under the derived pushforward and pullback of a morphism between algebraic stacks.