of the fake projective planes by these groups were studied by and also by . List of the 50 fake projective planes k is a totally real field. l is a totally imaginary quadratic extension of k, and ζ3 is a cube root of 1. T is a set of primes of k where a certain local subgroup is not hyperspecial. index is the index of the fundamental group in a certain arithmetic group. References External links Algebraic surfaces Complex surfaces