On the heart associated with a torsion pair

Abstract

Given an associative ring R and a torsion pair (T,F) in the category of right R-modules, the heartH(T,F) associated with (T,F) is an abelian subcategory of the bounded derived category Db(R). In the present paper we deal with the problem of when H(T,F) is equivalent to a category of modules. We show that if (T,F) is a faithful torsion pair, or, in the general case, if R is right poised and semiperfect, then H(T,F) is equivalent to a category of modules if and only if T and F are naturally associated with a complex in Db(R) of length two with finitely generated projective terms.