Verdier quotients of Calabi-Yau categories from quivers with potential

Abstract

We study a class of triangulated categories obtained as Verdier quotients of 3-Calabi-Yau categories combinatorially described by quivers with potential from (decorated) marked surfaces. We study their bounded t-structures and consider in particular the exchange graphs of hearts and silting objects, and show that the Koszul isomorphism between these graphs is preserved under Verdier quotient.

Final version to appear in Documenta Mathematica. v2: sections 5 and 6 expanded with details, list of notation added, minor modifications in the presentation