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arXiv · 1801.05355

A Local-global principle for isogenies of composite degree

Isabel Vogt
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Abstract

Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction of $E$ modulo that prime has rational cyclic isogeny of fixed degree, we can ask if this forces $E$ to have a cyclic isogeny of that degree over $K$. Building upon the work of Sutherland, Anni, and Banwait-Cremona in the case of prime degree, we consider this question for cyclic isogenies of arbitrary degree.

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Isabel Vogt. 2018-01-16. A Local-global principle for isogenies of composite degree. https://doi.org/10.1112/plms.12378

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