  The purpose of the present paper is to explain the fake projective plane
constructed by J.H. Keum from the point of view of arithmetic ball quotients.
Beside the ball quotient associated with the fake projective plane, we also
analize two further naturally related ball quotients whose minimal
desingularizations lead to two elliptic surfaces, one already considered by
J.H. Keum as well as the one constructed by M.N. Ishida in terms of p-adic
uniformization.
