On the distribution of supersingular primes for abelian surfaces

In 1976, Lang and Trotter conjectured the asymptotic growth for the number of primes p up to x for which the reduction of a non-CM elliptic curve E/Q at p is supersingular. Though the conjecture is still open, we now have unconditional upper and lower bounds thanks to the work of several mathematicians. However, less has been studied for the distribution of supersingular primes for abelian surfaces (even conjecturally). In this talk, I will present a recent work on unconditional upper bounds for the number of primes p up to x, for which the reduction of a fixed abelian surface at p is supersingular.