Perfect generation for regular algebraic stacks
arXiv:2601.04053
summary
The paper proves that for a regular Noetherian algebraic stack with quasi-finite diagonal, the derived category of complexes with quasi-coherent cohomology is generated by a single perfect complex, and in the concentrated case it is singly compactly generated.
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.
Sharpened results and exposition, comments welcome!
Topics & keywords
#derived categories#algebraic stacks#perfect complexes#compact generation#recollementperfect complexregular Noetherian stackquasi-finite diagonalcompactly generatedrecollementfiltration