Silting and cosilting classes in derived categories

JOURNAL OF ALGEBRA

卷:501

Article

Marks, Frederik¹  Vitoria, Jorge² 

[1] Univ Stuttgart, Inst Algebra & Zahlentheorie, Pfaffenwatdring 57, D-70569 Stuttgart, Germany

[2] City Univ London, Dept Math, Northampton Sq, London EC1V 0HB, England

关键词: Torsion pair;    t-structure;    Co-t-structure;    Silting complex;    Cosilting complex;    Derived category;   

DOI  :  10.1016/j.jalgebra.2017.12.031

来源: Elsevier

【 摘 要 】

An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are precisely the resolving and definable subcategories of the module category whose Ext-orthogonal class has bounded injective dimension. In this article, we prove a derived counterpart of the statements above in the context of silting theory Silting and cosilting complexes in the derived category of a ring generalise tilting and cotilting modules. They give rise to subcategories of the derived category, called silting and cosilting classes, which are part of both a t-structure and a co-t-structure. We characterise these subcategories: silting classes are precisely those which are intermediate and Ext-orthogonal classes to a set of compact objects, and cosilting classes are precisely the cosuspended, definable and co-intermediate subcategories of the derived category. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free