Explicit homotopy limits of dg-categories and twisted complexes

Block, Jonathan and Holstein, Julian V. S. and Wei, Zhaoting (2017) Explicit homotopy limits of dg-categories and twisted complexes. Homology, Homotopy and Applications, 19 (2). pp. 343-371. ISSN 1532-0073

[img]
Preview
PDF (1511 (2).08659v3)
1511_2_.08659v3.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (323kB)

Abstract

In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show that the totalization agrees with the homotopy limit in the following two cases: (1) the complexes of sheaves of $\mathcal O$-modules on the \v{C}ech nerve of an open cover of a ringed space $(X, \mathcal O)$; (2) the complexes of sheaves on the simplicial nerve of a discrete group $G$ acting on a space. The explicit models we obtain in this way are twisted complexes as well as their $D$-module and $G$-equivariant versions. As an application we show that there is a stack of twisted perfect complexes.

Item Type:
Journal Article
Journal or Publication Title:
Homology, Homotopy and Applications
Additional Information:
©2017 by International Press of Boston, Inc. All rights reserved.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2601
Subjects:
ID Code:
88643
Deposited By:
Deposited On:
13 Nov 2017 09:40
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Sep 2020 03:51