Séminaires : Séminaire d'Algèbre

We show that among the derived equivalent classes of homologically smooth and proper graded gentle algebras there is only one class whose perfect derived category does not admit silting objects.

As one application  we give a sufficient and necessary condition for any homologically smooth and proper graded gentle algebra under which all pre-silting objects in its perfect derived category may be complete into silting objects.
As another application we confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth and proper graded gentle algebras are a complete derived invariant. Hence, we obtain a complete invariant for partially wrapped Fukaya categories of surfaces with stops.
This is a report on joint work with Sibylle Schroll and Zhengfang Wang.

This talk will take place in hybrid mode at the Institut Henri Poincaré.