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 Thomason filtrations and the set 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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Acknowledgements
We are grateful for the excellent work environment and the assistance of the support staff of HRI, Prayagraj. The second author is supported in part by the INFOSYS scholarship. The authors thank the referee for carefully going through the manuscript and providing valuable comments and suggestions.
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Dubey, U.V., Sahoo, G. Compactly generated tensor t-structures on the derived categories of Noetherian schemes. Math. Z. 303, 100 (2023). https://doi.org/10.1007/s00209-023-03250-5
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DOI: https://doi.org/10.1007/s00209-023-03250-5