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Weirstrass points on Shimura curves

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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Date
2024-01-01
Student Status
Graduate
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Type of presentation
Oral Paper Presentation
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UVM Student Research Conference
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URI
https://hdl.handle.net/20.500.14849/8720
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Advisor(s)
Christelle Vincent
Department
Program/Major
Mathematics
College/School
College of Engineering and Mathematical Sciences
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Engineering and Math Science
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