Cancellations, additions and Lego - type constructions

The first part of my talk will deal with "non-classical" partial tilting modules, that is partial tilting modules T of projective dimension at most 2 with the following property: if Hom(T,X) = 0 and Ext*(T,X) = 0 for every * > 0 , then X = 0 . The second part of my talk will deal with partial tilting (but not tilting) modules T with the above property. As we shall see, there seems to be a weak relationship between the complexes T° and the indecomposable complexes orthogonal to them. For instance,some of these complexes look like mutations of direct summands of the complexes T°, while other are completely different.