Ordinary primes in Hilbert modular varieties

Joint IAS/Princeton University Number Theory Seminar
Topic:Ordinary primes in Hilbert modular varieties
Speaker:Junecue Suh
Affiliation:University of California, Santa Cruz
Date:Thursday, December 14
Time/Room:4:30pm - 5:30pm/Fine 214, Princeton University

The modular Jacobians decompose, up to isogeny, into the abelian varieties $X_f$ cut out by cuspforms $f$ of weight 2, and a conjecture attributed to Serre posits that $X_f$ has infinitely many ordinary primes. Similarly for the André motives in the Hilbert modular varieties for totally real fields, cut out by cuspforms of parallel weight 2. We report on some methods for verifying the conjecture that are effective for some cuspforms, together with some examples where they fall short.