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.

An error in Corollary 2.2 and its proof is corrected. To appear in AJM

References in corpus (3)

• On triangulated orbit categories
• Relative Singularity Categories
• A simultaneous generalization of mutation and recollement on a triangulated category

Cited by in corpus (5)

• Reductions of triangulated categories and simple-minded collections
• $q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories
• Tilting theory for Gorenstein rings in dimension one
• Silting reduction and Calabi--Yau reduction of triangulated categories
• Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations