Back to Search
Start Over
Explicit homotopy limits of dg-categories and twisted complexes
- Source :
- Homology Homotopy Appl. 19. (2017). no. 2. 343-371
- Publication Year :
- 2015
-
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.<br />Comment: v3: 22 pages, minor changes, to appear in Homology, Homotopy and Applications. v2: a new subsection (Section 4.5) is added on the stack of twisted perfect complexes
Details
- Database :
- arXiv
- Journal :
- Homology Homotopy Appl. 19. (2017). no. 2. 343-371
- Publication Type :
- Report
- Accession number :
- edsarx.1511.08659
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4310/HHA.2017.v19.n2.a17