Tuesday, September 22, 15:15, 7.527.

Enrico Sabatini (Padova),
Telescope Conjecture for Path Algebras over Commutative Rings

Abstract:
Path algebras over commutative rings provide a rich framework in which commutative algebra and representation theory interact. Many fundamental results, ranging from characterizations of distinguished subcategories to more advanced results, have been established in both the settings of commutative noetherian rings and hereditary finite-dimensional algebras. However, the techniques developed in these two contexts are, in general, quite different and do not readily transfer from one to the other. In this talk, we investigate the telescope conjecture for t-structures (TC) in the setting of representations of Dynkin quivers over commutative noetherian rings. Recall that (TC) asks whether every homotopically smashing t-structure is compactly generated. We first characterize the compactly generated t-structures in the derived category of such representations and then show that (TC) also holds in this broader setting.