This article is cited in 3 papers

DG-categories and simplicial bar complexes

Tomohide Terasoma

Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan

Abstract: We prove that the DG category $K\mathcal C_A$ of DG complexes in $\mathcal C_A$ assocaited to a DGA $A$, is homotopy equivalent to that of comodules over the bar complex of $A$. We introduce simplicial bar complexes to give the homotopy equivalence. As an application, we show that the category of comodules over the 0-th cohomology of the bar complex of the Deligne algebra is equivalent to that of variations of mixed Tate Hodge structures on an algebraic variety.

Key words and phrases: bar complex, DG-category, Deligne cohomology.

MSC: 14F43, 14F45

Received: September 30, 2008; in revised form December 29, 2009

Language: English

DOI: 10.17323/1609-4514-2010-10-1-231-267

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