DG-category and simplicial bar complex
Algebraic Geometry
2009-05-04 v1 K-Theory and Homology
Abstract
In this paper, we prove that the DG category of DG complex of DG category of a differential graded algebra A is homotopy equivalent to that of comodules over the simplicial bar complex of A. Under the assuption of connectedness of A, we show the homotopy category of A-connection is equivalent to comodules on the homology of bar complex. As an application, we construct coalgebras classifying nilpotent variation of mixed Tate Hodge structures on algebraic varieties.
Cite
@article{arxiv.0905.0096,
title = {DG-category and simplicial bar complex},
author = {Tomohide Terasoma},
journal= {arXiv preprint arXiv:0905.0096},
year = {2009}
}
Comments
LaTeX 36 pages, no figures