Geodesic
Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms
Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 271-279

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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 $\mathbb{Z}$ there will be $\mathbb{Q}$ -linear relations among the values of a canonical height pairing evaluated at a basis modulo torsion of $A(k)$ .
DOI : 10.4153/CMB-2004-027-5
Mots-clés : 11G10, 14K15 
Naumann, Niko. Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms. Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 271-279. doi: 10.4153/CMB-2004-027-5
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     author = {Naumann, Niko},
     title = {Linear {Relations} {Among} the {Values} of {Canonical} {Heights} from the {Existence} of {Non-Trivial} {Endomorphisms}},
     journal = {Canadian mathematical bulletin},
     pages = {271--279},
     year = {2004},
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     number = {2},
     doi = {10.4153/CMB-2004-027-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-027-5/}
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