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arXiv · 1303.3809

A local-global principle for isogenies of prime degree over number fields

Samuele Anni
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Abstract

We give a description of the set of exceptional pairs for a number field $K$, that is the set of pairs $(\ell, j(E))$, where $\ell$ is a prime and $j(E)$ is the $j$-invariant of an elliptic curve $E$ over $K$ which admits an $\ell$-isogeny locally almost everywhere but not globally. We obtain an upper bound for $\ell$ in such pairs in terms of the degree and the discriminant of $K$. Moreover, we prove finiteness results about the number of exceptional pairs.

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Samuele Anni. 2013-03-15. A local-global principle for isogenies of prime degree over number fields. https://doi.org/10.1112/jlms%2Fjdu002

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