2021/03/27 by James Tao, Tao, James, Roman Travkin +1
Mathematics · #14F10 #18F20 #22E67 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2103.15011
openalex publication_date 2021/03/27 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
Let G be a semisimple, simply connected algebraic group over an algebraically closed field of characteristic zero. We prove that the ∞-category of D-modules on the loop group of G is equivalent to the monoidal colimit of the ∞-categories of D-modules on the standard parahoric subgroups. This also follows from arXiv:2009.10998, but the present paper gives a simpler proof. The idea is to develop a combinatorial model for the path space of a simplicial complex, in which 'paths' are sequences of adjacent simplices, and to use a generalized version of hyperdescent for D-modules. We also give two more applications of this hyperdescent theorem: triviality of D-modules on the 'schematic Bruhat-Tits building,' which was first established by Varshavsky using a different method, and triviality of D-modules on the `simplicial affine Springer resolution.'