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

Christelle Vincent

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

Number Theory 2015-04-17 v2

Authors: Christelle Vincent

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 $X_0(\mathfrak{p})$ .

Cite

@article{arxiv.1409.7466,
  title  = {Weierstrass points on the Drinfeld modular curve $X_0(\mathfrak{p})$},
  author = {Christelle Vincent},
  journal= {arXiv preprint arXiv:1409.7466},
  year   = {2015}
}

Comments

Main theorem has been strengthened. Mistakes in the proof of Theorems 5.7 and 6.2 have been fixed. A new section on the behavior of W(z) at the cusps has been added. Various typos corrected and clarifications made

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

Abstract

Cite

Comments

Related papers