Perfect generation for regular algebraic stacks

Abstract

We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect complex. In the concentrated case, the category is singly compactly generated. Key ingredients in the proofs include gluing generators along recollement and the use of suitable filtrations and presentations of the algebraic stack.

arXiv commentSharpened results and exposition, comments welcome!