Weierstrass points on the Drinfeld modular curve X_0(\mathfrak{p})

Algebra Seminar
Wednesday, April 13, 2011 - 1:00pm
1 hour (actually 50 minutes)
Skiles 006
University of Wisconsin Madison
For q a power of a prime, consider the ring \mathbb{F}_q[T]. Due to the many similarities between \mathbb{F}_q[T] and the ring of integers \mathbb{Z}, we can define for \mathbb{F}_q[T] objects that are analogous to elliptic curves, modular forms, and modular curves. In particular, for \mathfrak{p} a prime ideal in \mathbb{F}_q[T], we can define the Drinfeld modular curve X_0(\mathfrak{p}), and study the reduction modulo \mathfrak{p} of its Weierstrass points, as is done in the classical case by Rohrlich, and Ahlgren and Ono. In this talk we will present some partial results in this direction, defining all necessary objects as we go. The first 20 minutes should be accessible to graduate students interested in number theory.