Perfect generation for regular algebraic stacks
Pat Lank
TL;DR
This paper proves that the derived category of certain regular algebraic stacks can be generated by a single perfect complex, simplifying the understanding of their categorical structure.
Contribution
It establishes that for regular Noetherian algebraic stacks with quasi-finite diagonal, the derived category is generated by one perfect complex, extending known results to a broader class.
Findings
Derived category is generated by a single perfect complex.
In the concentrated case, the category is singly compactly generated.
Uses gluing generators and filtrations in the proofs.
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics