Heegner points and Mordell-Weil groups of elliptic curves over large fields

Bo-Hae Im

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Heegner points and Mordell-Weil groups of elliptic curves over large fields

Bo-Hae Im

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Abstract

Let $E/\bbq$ be an elliptic curve defined over $\bbq$ with conductor $N$ and $\gq$ the absolute Galois group of an algebraic closure $\bar{\bbq}$ of $\bbq$. We prove that for every $σ\in \gq$, the Mordell-Weil group $E(\oqs)$ of $E$ over the fixed subfield of $\bar{\bbq}$ under $σ$ has infinite rank. Our approach uses the modularity of $E/\bbq$ and a collection of algebraic points on $E$ -- the so-called {\em Heegner points} -- arising from the theory of complex multiplication.

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Bo-Hae Im. 2004-11-25. Heegner points and Mordell-Weil groups of elliptic curves over large fields. https://arxiv.org/abs/math/0411534

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