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arXiv · 1405.2108

There are genus one curves of every index over every infinite, finitely generated field

Pete L. Clark·Allan Lacy
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Abstract

Every nontrivial abelian variety over a Hilbertian field in which the weak Mordell-Weil theorem holds admits infinitely many torsors with period any $n > 1$ which is not divisible by the characteristic. The corresponding statement with "period" replaced by "index" is plausible but much more challenging. We show that for every infinite, finitely generated field $K$, there is an elliptic curve $E_{/K}$ which admits infinitely many torsors with index any $n > 1$.

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Pete L. Clark, Allan Lacy. 2014-05-08. There are genus one curves of every index over every infinite, finitely generated field. https://arxiv.org/abs/1405.2108

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