Compactly generated tensor t-structures on the derived category of a Noetherian scheme

Gopinath Sahoo; Umesh V. Dubey

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arXiv · 2204.05015

Compactly generated tensor t-structures on the derived category of a Noetherian scheme

Gopinath Sahoo·Umesh V. Dubey

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Abstract

We introduce a tensor compatibility condition for t-structures. For any Noetherian scheme $X$, we prove that there is a one-to-one correspondence between the set of filtrations of Thomason subsets and the set of aisles of compactly generated tensor compatible t-structures on the derived category of $X$. This generalizes the earlier classification of compactly generated t-structures for commutative rings to schemes. Hrbek and Nakamura have reformulated the famous telescope conjecture for t-structures. As an application of our main theorem, we prove that a tensor version of the conjecture is true for separated Noetherian schemes.

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BibTeX RIS

Gopinath Sahoo, Umesh V. Dubey. 2022-04-11. Compactly generated tensor t-structures on the derived category of a Noetherian scheme. https://arxiv.org/abs/2204.05015

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