Homomorphisms of complexes via homologies

Intan Muchtadi-Alamsyah

Abstract:

By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from
projective modules over the first ring such that the second ring is the endomorphism ring of this
tilting complex.

 In this work I describe, under some conditions, the homomorphism space in the derived category between
two complexes as iterated pull-back of homomorphism spaces between the homologies of the complexes.