Compact Support Cohomology of Picard Modular Surfaces

2016/01/04 by Jukka Petri Mikael Keranen, Keranen, Jukka
Mathematics · #11R39 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1601.00576

openalex publication_date 2016/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the cohomology with compact supports of a Picard modular surface as a virtual module over the product of the appropriate Galois group and the appropriate Hecke algebra. We use the method developed by Ihara, Langlands, and Kottwitz: comparison of the Grothendieck-Lefschetz formula and the Arthur-Selberg trace formula. Our implementation of this method takes as its starting point the works of Laumon and Morel.

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