# zbMATH — the first resource for mathematics

A note on height pairings on polarized abelian varieties. (English) Zbl 1016.14025
Summary: Let $$A$$ be an abelian variety defined over a number field $$k$$. In this short note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.

##### MSC:
 14K05 Algebraic theory of abelian varieties 14G40 Arithmetic varieties and schemes; Arakelov theory; heights