Geodesic
Explicit homotopy limits of $\mathrm{dg}$-categories and twisted complexes
Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 343-371.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper we study the homotopy limits of cosimplicial diagrams of $\mathrm{dg}$-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 Čech 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.
DOI : 10.4310/HHA.2017.v19.n2.a17
Classification : 14F05, 18D20, 18G55
Keywords: differential graded category, twisted complex 
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     author = {Jonathan Block and Julian Holstein and Zhaoting Wei},
     title = {Explicit homotopy limits of $\mathrm{dg}$-categories and twisted complexes},
     journal = {Homology, homotopy, and applications},
     pages = {343--371},
     publisher = {mathdoc},
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     number = {2},
     year = {2017},
     doi = {10.4310/HHA.2017.v19.n2.a17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a17/}
}
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Jonathan Block; Julian Holstein; Zhaoting Wei. Explicit homotopy limits of $\mathrm{dg}$-categories and twisted complexes. Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 343-371. doi : 10.4310/HHA.2017.v19.n2.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a17/

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