Deligne-Beilinson Cohomology of Affine Groups

2015/07/11 by Richard Hain, Hain, Richard
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1507.03144

openalex publication_date 2015/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to develop the theory of Deligne-Beilinson cohomology of affine groups with a mixed Hodge structure. The motivation comes from Hodge theory and the study of motives, where such groups appear. Several of Francis Brown's period computations (arXiv:1407.5167) are interpreted as elements of the DB cohomology of the relative unipotent completion of SL₂(Z) and their cup products. The results in this paper are used in arXiv:1403.6443 where they are used to prove that Pollack's quadratic relations are motivic.

Cited by

• Multiple Modular Values and the relative completion of the fundamental group of M_1,1

Related

• Deligne--Beilinson cohomology and log Hodge theory
• Line bundles, connections, Deligne-Beilinson and absolute Hodge cohomology
• Mixed Hodge Structures
• Réalisations de Hodge des motifs de Voevodsky
• A K-theoretic interpretation of real Deligne cohomology