Arithmetic Geometry and Number Theory RTG Seminar: Ordinary primes in Hilbert modular varieties

Seminar | April 9 | 3:10-5 p.m. | 748 Evans Hall

 Junecue Suh, UCSC

 Department of Mathematics

A well-known conjecture (often attributed to Serre) asserts that any motive over any number field has infinitely many ordinary primes, in the sense of the Newton Polygon coinciding with the Hodge Polygon. We will present a few methods for producing more ordinary primes in the case of modular Jacobians — and more generally the part of the (intersection) cohomology of Hilbert modular varieties cut out by cusp forms. If time permits, we will also discuss examples in which our methods fall short.

Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.