Arithmetic of a fake projective plane and related elliptic surfaces (Q612857)

Summary: The purpose of the present paper is to explain the fake projective plane constructed by \textit{J. Keum} [Topology 45, No. 5, 919--927 (2006; Zbl 1099.14031)] from the point of view of arithmetic ball quotients . Beside the ball quotient associated with the fake projective plane, we also analyze two further naturally related ball quotients whose minimal desingularizations lead to two elliptic surfaces, one already considered by J. Keum as well as the one constructed by \textit{M. N. Ishida} [Tohoku Math J. 40, 367--398 (1988; Zbl 0694.14017)] in terms of \(p\)-adic uniformization.