Perfectly generated $t$-structures for algebraic stacks

TL;DR

This paper classifies certain tensor-compatible t-structures generated by perfect complexes on algebraic stacks, extending known classifications from affine schemes to stacks using Thomason filtrations.

Contribution

It introduces a classification of t-structures on algebraic stacks generated by perfect complexes, based on Thomason filtrations, generalizing affine scheme results.

Findings

Classified t-structures generated by perfect complexes on algebraic stacks.

Extended affine scheme classification results to algebraic stacks.

Utilized Thomason filtrations for the classification process.

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 \`{a} la Hrbek for the affine scheme case.