Algebra Seminar

calendars.uark.edu

Speaker: Wanlin Li (Vanderbilt University) Title: 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. In the opposite direction, Elkies proved that an elliptic curve defined 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 defined 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. Following the seminar, participants are warmly invited to join the speaker for dinner. If you would like to attend, please email John Bergdall (bergdall@uark.edu) or speak with one of the seminar organizers during the event. Other details about the algebra seminar can be found athttps://math-colloquium.uark.edu/algebra-research-seminar/.