2009/05/01 by Tomohide Terasoma, Terasoma, Tomohide
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.0905.0096
openalex publication_date 2009/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.