Construction of 𝑡-structures and equivalences of derived categories

Tarrío, Leovigildo Alonso; López, Ana Jeremías; Salorio, María José

doi:10.1090/S0002-9947-03-03261-6

Construction of $t$-structures and equivalences of derived categories
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by Leovigildo Alonso Tarrío, Ana Jeremías López and María José Souto Salorio

Trans. Amer. Math. Soc. 355 (2003), 2523-2543

DOI: https://doi.org/10.1090/S0002-9947-03-03261-6

Published electronically: January 30, 2003

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Abstract:

We associate a $t$-structure to a family of objects in $\boldsymbol {\mathsf {D}}(\mathcal {A})$, the derived category of a Grothendieck category $\mathcal {A}$. Using general results on $t$-structures, we give a new proof of Rickard’s theorem on equivalence of bounded derived categories of modules. Also, we extend this result to bounded derived categories of quasi-coherent sheaves on separated divisorial schemes obtaining, in particular, Beĭlinson’s equivalences.

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