### Arithmetic of the Legendre curve

- Series
- Algebra Seminar
- Time
- Monday, March 7, 2011 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Doug Ulmer – Georgia Tech

Let k be a field (not of characteristic 2) and let t be an
indeterminate. Legendre's elliptic curve is the elliptic curve over k(t)
defined by y^2=x(x-1)(x-t). I will discuss the arithmetic of this curve
(group of solutions, heights, Tate-Shafarevich group) over the
extension fields k(t^{1/d}). I will also mention several variants and
open problems which would make good thesis topics.