Perfectly generated $t$-structures for algebraic stacks
Algebraic Geometry
2025-07-04 v3 Commutative Algebra
Abstract
This work studies -structures for the derived category of quasi-coherent sheaves on a quasi-compact quasi-separated algebraic stack. Specifically, using Thomason filtrations, we classify those -structures which are generated by perfect complexes and satisfy a tensor compatibility. Interestingly, the only input required is the classification \`{a} la Hrbek for the affine scheme case.
Cite
@article{arxiv.2506.18803,
title = {Perfectly generated $t$-structures for algebraic stacks},
author = {Pat Lank},
journal= {arXiv preprint arXiv:2506.18803},
year = {2025}
}
Comments
Current: Refinement to qcqs case and details added. Previous: Upgrade to qcqs stacks by using only Hrbek's affine result