Classification and nonexistence for $t$-structures on derived categories of schemes
Abstract: This work establishes new results on the classification of $t$-structures for many subcategories of the derived category of quasi-coherent sheaves on a Noetherian scheme. Our work makes progress in two different directions. On one hand, we provide an improvement of a result of Takahashi on $t$-structures, generalizing it to the case of the bounded derived category of coherent sheaves on a quasi-compact CM-excellent scheme of finite Krull dimension. On the other hand, via independent techniques, we prove a variation of a recent result of Neeman which resolved a conjecture of Antieau, Gepner, and Heller.
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- Compactly generated tensor t-structures on the derived categories of Noetherian schemes. Math. Z., 303(4):Paper No. 100, 22pp, 2023.
- Amnon Neeman. Bounded t-structures on the category of perfect complexes. Acta Math (to appear). arxiv:2202.08861v3.
- Harry Smith. Bounded t-structures on the category of perfect complexes over a noetherian ring of finite krull dimension. Adv. Math, 399:Paper No. 108241, 21pp, 2022.
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