A remark on a conjecture of Buzzard-Gee and the cohomology of Shimura varieties

2012/06/28 by Christian Johansson, Johansson, Christian
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1206.6730

10 pages, minor corrections and changes to presentation

openalex publication_date 2012/06/28 · arxiv created 2013/01/29 · arxiv updated 2013/01/30 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We compare the conjecture of Buzzard-Gee on the association of Galois representations to C-algebraic automorphic representations with the conjectural description of the cohomology of Shimura varieties due to Kottwitz, and the reciprocity law at infinity due to Arthur. This is done by extending Langlands's representation of the L-group associated with a Shimura datum to a representation of the C-group of Buzzard-Gee. The approach offers an explanation of the explicit Tate twist appearing in Kottwitz's description.

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