2014/11/05 by Daniel Allcock, Fumiharu Kato, Allcock, Daniel +1
Computer Science · Mathematics · #11F23 #14J25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Topological and Geometric Data Analysis #advanced mathematical theories #math.AG #math.GR #msc:11F23 #msc:14J25
paper · pdf · doi:10.48550/arxiv.1411.1140
17 pages
arxiv created 2014/11/05 · openalex publication_date 2014/11/05 · arxiv updated 2014/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in PGL3(Q2) that has nontrivial torsion. It turns out to be a fake projective plane, commensurable with Mumford's fake plane yet distinct from it and the other fake planes that arise from 2-adic uniformization by torsion-free groups. As part of the proof, and of independent interest, we compute the homotopy type of the Berkovich space of our plane.