Arithmetic structure of CMSZ fake projective planes

2000/06/29 by Fumiharu Kato, Kato, Fumiharu, Hiroyuki Ochiai +1
Computer Science · Engineering · Mathematics · #11G15 #11Q25 #14G35 #14J29 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.AG #msc:11G15 #msc:11Q25 #msc:14G35 #msc:14J29

paper · pdf · doi:10.48550/arxiv.math/0006223

14 pages, LaTeX2e + Euler font

arxiv created 2000/06/29 · openalex publication_date 2000/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the fake projective planes constructed from the diadic discrete group discovered by Cartwright, Mantero, Steger, and Zappa are connected Shimura varieties associated to a certain unitary group. The necessary Shimura data, as well as the unitary group, are explicitly described. We also give a field of definition of these fake projective planes.

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