On the heart associated with a torsion pair

Given an associative ring R and a torsion pair ( T , F ) in the category of right R-modules, the heart H ( T , F ) associated with ( T , F ) is an abelian subcategory of the bounded derived category D b ( 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 D b ( R ) of length two with finitely generated projective terms.