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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_2004_027_5,
     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},
     volume = {47},
     number = {2},
     doi = {10.4153/CMB-2004-027-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-027-5/}
}
TY  - JOUR
AU  - Naumann, Niko
TI  - Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 271
EP  - 279
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-027-5/
DO  - 10.4153/CMB-2004-027-5
ID  - 10_4153_CMB_2004_027_5
ER  - 
%0 Journal Article
%A Naumann, Niko
%T Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms
%J Canadian mathematical bulletin
%D 2004
%P 271-279
%V 47
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-027-5/
%R 10.4153/CMB-2004-027-5
%F 10_4153_CMB_2004_027_5

[FLSSSW] [FLSSSW] Flynn, E., Leprévost, F., Schaefer, E., Stein, W., Stoll, M. and Wetherell, J., Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves. Math. Comp. (236) 70 (2001), 1675–1697. Google Scholar

[La] [La] Lang, S., Fundamentals of Diophantine Geometry. Springer, New York, 1983. Google Scholar

[Mi2] [Mi2] Milne, J. S., On the Arithmetic of Abelian Varieties. Invent.Math. 17 (1972), 177–190. Google Scholar

[Mu] [Mu] Mumford, D., Abelian Varieties. Tata Inst. Fund. Res. Stud. Math. 5, Oxford University Press, 1974. Google Scholar

[Ne] [Ne] Néron, A., Quasi-fonctions et Hauteurs sur les variétés abéliennes. Ann. of Math. 82 (1965), 249–331. Google Scholar

[Se] [Se] Serre, J.-P., Lectures on the Mordell-Weil Theorem. Aspects Math. E15, Vieweg, Braunschweig, 1989. Google Scholar

[Ta] [Ta] Talamanca, V., A note on height pairings on polarized abelian varieties. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 10 (1999), 57–60. Google Scholar

Cité par Sources :