Tilting and torsion pairs in module, functor and derived categories.

We consider tilting torsion pairs induced by infinitely generated tilting modules over an associative ring. Every tilting torsion class of modules is a definable class, but we produce examples of non tilting definable torsion classes over commutative valuation domains.

Among the hereditary torsion pairs of finite type in the functor category, we characterize the ones associated to tilting torsion pairs. In particular, we establish when they are TTF (torsion-torsion free) triples and we give applications to the case of commutative domains.  

We also consider the functors induced by a tilting module between the derived category of the ring and the derived category of the endomorphism ring.

Silvana Bazzoni