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Linear relations among the values of canonical heights from the existence of non-trivial endomorphisms

Niko Naumann
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Abstract

We study the interplay between canonical heights and endomorphisms of an abelian variety $A$ over a number field $k$. In particular we show that whenever the ring of endomorphisms defined over $k$ is strictly larger than $\Z$ there will be $\Q$-linear relations among the values of a canonical height-pairing evaluated at a basis modulo torsion of $A(k)$.

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Niko Naumann. 2003-01-05. Linear relations among the values of canonical heights from the existence of non-trivial endomorphisms. https://arxiv.org/abs/math/0205104

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