Publications [#320425] of Richard Hain

Papers Published

1. Hain, R, Deligne-Beilinson Cohomology of Affine Groups, in Hodge Theory and $L^2$-analysis, edited by Ji, L (2017), International Press, ISBN 9781571463517 [arXiv:1507.03144]
   (last updated on 2025/04/05)

   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 $SL_2(Z)$ 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.