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

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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:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 88643
Deposited By: ep_importer_pure
Deposited On: 13 Nov 2017 09:40
Refereed?: Yes
Published?: Published
Last Modified: 17 Feb 2020 03:45
URI: https://eprints.lancs.ac.uk/id/eprint/88643

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