Weierstrass points on the Drinfeld modular curve $X_0(\mathfrak{p})$

Christelle Vincent

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arXiv · 1409.7466

Weierstrass points on the Drinfeld modular curve $X_0(\mathfrak{p})$

Christelle Vincent

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Abstract

Consider the Drinfeld modular curve $X_0(\mathfrak{p})$ for $\mathfrak{p}$ a prime ideal of $\mathbb{F}_q[T]$. It was previously known that if $j$ is the $j$-invariant of a Weierstrass point of $X_0(\mathfrak{p})$, then the reduction of $j$ modulo $\mathfrak{p}$ is a supersingular $j$-invariant. In this paper we show the converse: Every supersingular $j$-invariant is the reduction modulo $\mathfrak{p}$ of the $j$-invariant of a Weierstrass point of $X_0(\mathfrak{p})$.

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Christelle Vincent. 2014-09-26. Weierstrass points on the Drinfeld modular curve $X_0(\mathfrak{p})$. https://arxiv.org/abs/1409.7466

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