Rational points on modular curves via the moduli interpretation

Abstract: In theory, Chabauty-Coleman provides an explicit method to obtain rational points on any curve, so long as its genus exceeds its Mordell-Weil rank. In practice, when applied to modular curves, we often encounter difficulties in finding a suitable plane model, which only worsens as the genus increases. In this talk we describe how to skip this step and instead work directly with the coarse moduli space. This is joint work with Steve Huang and Jun Bo Lau.

number theory

Audience: researchers in the topic

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.