Weirstrass points on Shimura curves
Conference Year
2024
Abstract
In this talk we introduce Weierstrass points on curves, which we can think of as the zeros of a certain Wronskian on the curve. We then recall results of Rohrlich and Ahlgren-Ono that show that on the curve $X_0(p)$, for $p$ a prime, the reduction of this Wronskian modulo $p$ is a power of the Hasse invariant. Finally, we discuss the generalization of these results to the setting of Shimura curves parametrizing abelian surfaces with quaternionic multiplication.
Primary Faculty Mentor Name
Christelle Vincent
Status
Graduate
Student College
College of Engineering and Mathematical Sciences
Program/Major
Mathematics
Primary Research Category
Engineering and Math Science
Weirstrass points on Shimura curves
In this talk we introduce Weierstrass points on curves, which we can think of as the zeros of a certain Wronskian on the curve. We then recall results of Rohrlich and Ahlgren-Ono that show that on the curve $X_0(p)$, for $p$ a prime, the reduction of this Wronskian modulo $p$ is a power of the Hasse invariant. Finally, we discuss the generalization of these results to the setting of Shimura curves parametrizing abelian surfaces with quaternionic multiplication.