Explicit homotopy limits of dg-categories and twisted complexes
| Autor: | Block, Jonathan, Holstein, Julian V. S., Wei, Zhaoting |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Homology Homotopy Appl. 19. (2017). no. 2. 343-371 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4310/HHA.2017.v19.n2.a17 |
| Popis: | 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. 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 |
| Databáze: | arXiv |
| Externí odkaz: |
|