Background
Type: Article

Specifying the Auslander-Reiten translation for complexes of modules

Journal: Forum Mathematicum (09337741)Year: 1 March 2016Volume: 28Issue: Pages: 377 - 389
DOI:10.1515/forum-2013-0209Language: English

Abstract

We describe explicitly the Auslander-Reiten translation in the category of bounded complexes of finitely generated maximal Cohen-Macaulay modules, Cb(CM R), over a commutative local Cohen-Macaulay ring R with a canonical module ω. Then the Auslander-Reiten formula is generalized for complexes in Cb(CM R) and we prove the existence theorem of Auslander-Reiten sequences. As an application of our results, we investigate the existence of Auslander-Reiten triangles in the category of perfect complexes as a full triangulated subcategory of Db(mod R). © 2016 by De Gruyter 2016.


Author Keywords

adjoin pairAuslander-Reiten sequenceshomotopy categorymaximal Cohen-Macaulay modules