Silting and cosilting classes in derived categories

被引:24
|
作者
Marks, Frederik [1 ]
Vitoria, Jorge [2 ]
机构
[1] Univ Stuttgart, Inst Algebra & Zahlentheorie, Pfaffenwatdring 57, D-70569 Stuttgart, Germany
[2] City Univ London, Dept Math, Northampton Sq, London EC1V 0HB, England
基金
英国工程与自然科学研究理事会;
关键词
Torsion pair; t-structure; Co-t-structure; Silting complex; Cosilting complex; Derived category;
D O I
10.1016/j.jalgebra.2017.12.031
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
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.
引用
收藏
页码:526 / 544
页数:19
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