2022/02/02 by Damien Junger, Junger, Damien
Mathematics · #11G18 #Advanced Topics in Algebra #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2202.01018
openalex publication_date 2022/02/02 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/04
The goal of this work is to study some aspects of the geometry of the first cover Σ1 in the Drinfeld tower over ℍdK the Drinfeld symmetric space over K a finite extension of ℚp. It is a cyclic étale cover of order prime to p and even of Kummer type from the vanishing of the Picard group of ℍdK shown in a previous work of the author. It is then completely described by a certain class of invertible functions on ℍdK via the Kummer exact sequence and the main result of this article gives an explicit description of this class thus providing "equations" for Σ1. This statement extends and uses crucially the local description over a vertex obtained by Wang (and originally by Teitelbaum in dimension 1). One of the main consequence of our global equation is the description of invertible functions of Σ1 in terms of the invertible functions of ℍdK.