2021/11/19 by Damien Junger, Junger, Damien
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2111.10274
openalex publication_date 2021/11/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this article, we give an explicit description of the invertible functions\non the Drinfeld symmetric space over K a finite extension of \ℚp.\nWe identify them with some distribution spaces over the profinite set of\nK-rationnal points of the projective space. The strategy consists of\nconstructing a map from these distributions to the invertible functions\nfollowing the methods of Schneider-Stuhler, Iovita-Spiess, de Shalit. We show\nthat it is compatible with the isomorphisms they constructed to compute 'etale\nand de Rham cohomology in degree 1 and that this property forces our desired\nmap to be an isomorphism. In particular, we get a \ℤ-structure on\nthese cohomology groups.\n