Construction of 𝑡-structures and equivalences of derived categories

Abstract

We associate a t t -structure to a family of objects in D ( A ) \boldsymbol {\mathsf {D}}(\mathcal {A}) , the derived category of a Grothendieck category A \mathcal {A} . Using general results on t 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.