Perfectly generated $t$-structures for algebraic stacks

This work studies $t$-structures for the derived category of quasi-coherent sheaves on a quasi-compact quasi-separated algebraic stack. Specifically, using Thomason filtrations, we classify those $t$-structures which are generated by perfect complexes and satisfy a tensor compatibility. Interestingly, the only input required is the classification à la Hrbek for the affine scheme case.

Publication Details

Journal
ArXiv.org
Published
2025-06-23
Primary Topic
Algebraic structures and combinatorial models
Type
article
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article

Perfectly generated $t$-structures for algebraic stacks

ArXiv.org
Algebraic structures and combinatorial models
article

Perfectly generated $t$-structures for algebraic stacks

article en

Abstract

This work studies $t$-structures for the derived category of quasi-coherent sheaves on a quasi-compact quasi-separated algebraic stack. Specifically, using Thomason filtrations, we classify those $t$-structures which are generated by perfect complexes and satisfy a tensor compatibility. Interestingly, the only input required is the classification à la Hrbek for the affine scheme case.

ArXiv.org
Openalex Percentile: Top 43%
Algebraic structures and combinatorial models
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Perfectly generated $t$-structures for algebraic stacks · ArXiv.org (2025) | TGRS Research Map | TGRS