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arXiv · 2006.02538

Explicit height bounds for $K$-rational points on transverse curves in powers of elliptic curves

Francesco Veneziano·Evelina Viada
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Abstract

Let $C$ be an algebraic curve embedded transversally in a power $E^N$ of an elliptic curve $E$. In this article we produce a good explicit bound for the height of all the algebraic points on $C$ contained in the union of all proper algebraic subgroups of $E^N$. The method gives a totally explicit version of the Manin-Dam'janenko Theorem in the elliptic case and it is a generalisation of previous results only proved when $E$ does not have Complex Multiplication.

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Francesco Veneziano, Evelina Viada. 2020-06-03. Explicit height bounds for $K$-rational points on transverse curves in powers of elliptic curves. https://doi.org/10.2140/pjm.2021.315.477

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