- Series
- Algebra Seminar
- Time
- Wednesday, April 13, 2011 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Christelle Vincent – University of Wisconsin Madison
- Organizer
- Matt Baker
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.