REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Alberto Tonolo

ABSTRACT: Let R be an arbitrary associative ring and P be a complex of finitely generated projective R-modules of term length two in the derived category D(R). In 2002 Hoshino, Kato and Miyachi showed that, under suitable conditions, P induces a torsion theory in R-Mod, whose associated t-structure has the heart equivalent to the module category over the ring End(P). In a recent joint paper with Francesca Mantese we have proved, for a wide class of rings, that if the heart of the t-structure associated with a torsion pair in R-Mod is equivalent to a module category, then necessarily this torsion pair is induced by  a complex of finitely generated projective R-modules of term length two. In this talk I will describe the Hoshino, Kato and Miyachi results and the main ideas of what I obtained in collaboration with Francesca.