The densest lattices in PGL3(Q2)

2011/05/10 by Daniel Allcock, Fumiharu Kato, Allcock, Daniel +1
Mathematics · #22E40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1105.1860

openalex publication_date 2011/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We find the smallest possible covolume for lattices in PGL3(Q2), show that there are exactly two lattices with this covolume, and describe them explicitly. They are commensurable, and one of them appeared in Mumford's construction of his fake projective plane. We also discuss a new 2-adic uniformization of another fake projective plane.

Citations

• Lattices in complete rank 2 Kac-Moody groups

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