Weirstrass points on Shimura curves
Chaos, HollyPaige
Chaos, HollyPaige
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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.
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Graduate
Date
2024-01-01