Tuesday, June 8, 14:00

Michal Hrbek (Czech Academy of Sciences, Prague)
Tilting objects induced by codimension functions on Spec(R)

Abstract:
We consider silting t-structures induced by special filtrations of the Zariski spectrum of a commutative noetherian ring, the slice filtrations. We show that the associated silting objects can in this case be constructed very explicitly, allowing us to study conditions under which these objects are tilting (and thus yield derived equivalences). It turns out that if the ring admits a dualizing complex, these silting objects are tilting if and only if the slice filtration is induced by a codimension function on Spec(R). In the absence of a dualizing complex, the situation is more complicated - the tilting property of the t-structure induced by a codimension function is tied to certain good geometric properties of the ring. This is a report on an ongoing joint work with Tsutomu Nakamura and Jan Šťovíček.