Primes of superspecial reduction for QM abelian surfaces

摘要

We show that any abelian surface with multiplication by the quaternion Q-algebra of discriminant 6, with field of moduli Q and which is a Jacobian in characteristic 2 and 3, has infinitely many primes of superspecial reduction. This is done by examining complex multiplication points in characteristic 0 and p and the values of a certain j-function on the associated moduli space at these points.