Linear relations among the values of canonical heights from the existence of non-trivial endomorphisms
Abstract
Description
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 $A(k)$.
14 pages, exposition improved, to appear in Bulletin of the Canadian Mathematical Society
14 pages, exposition improved, to appear in Bulletin of the Canadian Mathematical Society