Colloquium: Reductions of abelian varieties

Abstract: Given an abelian variety defined over a number field, a conjecture attributed to Serre predicts that its set of ordinary primes is of positive density. This conjecture had been proved for elliptic curves, abelian surfaces, and certain higher dimensional abelian varieties following the work of Serre, Katz, Ogus, Pink, Sawin, Suh, Fite, etc. On the opposite direction, Elkies proved that an elliptic curve over Q has infinitely many supersingular reductions. The generalization of the 0-dimensional supersingular locus of the modular curve is the so-called basic locus of a Shimura curve at a good prime. In this talk, I will discuss the set of basic primes for some abelian varieties over totally real fields parametrized by certain unitary Shimura curves; these Shimura curves arise from the moduli spaces of cyclic covers of the projective line ramified at 4 points.

Host: Matt Kerr

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00pm to 3:00pm