Philadelphia Area Number Theory Seminar

Wednesday, October 30, 2019 - 2:15pm

Yunqing Tang

Princeton University

Given an abelian surface (or the Jacobian of a genus two curve) over the field of rationals with trivial geometric endomorphism ring, Achter and Howe proved that the set of primes modulo which the abelian surface is not geometrically isogenous to the product of two elliptic curves is of density 0. They provided a heuristic which indicates that the number of such primes less than X is almost X1/2. Under certain technical assumptions, we prove that at least this set is infinite. This is joint work with Ananth Shankar, Arul Shankar and Salim Tayou.