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arXiv · 2101.02293

Most Elliptic Curves over Global Function Fields are Torsion Free

Tristan Phillips
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Abstract

Given an elliptic curve $E$ over a global function field $K$, the Galois action on the $n$-torsion points of $E$ gives rise to a mod-n Galois representation $\rho_{E,n}$. For $K$ satisfying some mild conditions, we show that the set of $E$ for which $\rho_{E,n}$ is as large as possible for all $n$, has density $1$.

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Tristan Phillips. 2021-01-06. Most Elliptic Curves over Global Function Fields are Torsion Free. https://arxiv.org/abs/2101.02293

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