Quotients of triangulated categories and Equivalences of Buchweitz, Orlov and Amiot--Guo--Keller

Abstract

We give a sufficient condition for a Verdier quotient $\ct/\cs$ of a triangulated category $\ct$ by a thick subcategory $\cs$ to be realized inside of $\ct$ as an ideal quotient. As applications, we deduce three significant results by Buchweitz, Orlov and Amiot--Guo--Keller.