Geodesic
Height on families of Abelian varieties
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 169-179 
Yu. G. Zarhin; Yu. I. Manin. Height on families of Abelian varieties. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 169-179. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a0/
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     author = {Yu. G. Zarhin and Yu. I. Manin},
     title = {Height on families of {Abelian} varieties},
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     volume = {18},
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     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X$ be an Abelian variety imbedded in projective space, and let $L$ be an induced invertible sheaf on $X$. In this paper explicit bounds are determined for the difference $\widehat h_L-h_L$, where $\widehat h_L$ is the Neron–Tate height and $h_L$ is the Weil height. Bibliography: 5 titles.

[1] V. A. Demyanenko, “Otsenka ostatochnogo chlena v formule Teita”, Matem. zametki, 3:3 (1968), 271–278 | Zbl

[2] S Lang, Diophantine Geometry, Interscience, New York, 1962 | MR

[3] Yu. I. Manin, “Teorema Mordella–Veilya”, Prilozhenie k kn.: D. Mamford, Abelevy mnogoobraziya, Mir, Moskva, 1971

[4] Yu. I. Manin, “Krugovye polya i modulyarnye krivye”, Uspekhi matem. nauk, XXVI:6(162) (1971), 7–71 | MR

[5] D. Mumford, “On the equations defining abelian varieties. I”, Invent. Math., 1:4 (1966), 287–354 ; Matematika, 14:1 (1970), 104–136; 14:2 (1970), 3–34 | DOI | MR | Zbl