Construction of t-structures and equivalences of derived categories

Leovigildo Alonso, Ana Jeremias, Ma. -Jose Souto

Published 2002-03-01, updated 2002-10-22Version 3

We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category 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, Beilinson's equivalences.