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

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

2002-05-10

arxiv.org/abs/math/0205104v2

Mathematics

Algebraic Geometry

14 pages, exposition improved, to appear in Bulletin of the Canadian Mathematical Society

Scientific paper

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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