Theta height and Faltings height
Copyright policy )Theta height and Faltings height
Using original ideas from J.-B. Bost and S. David, we provide an explicit comparison between the Theta height and the stable Faltings height of a principally polarized abelian variety. We also give as an application an explicit upper bound on the number of K-rational points of a curve of genus g>1 over a number filed K under a conjecture of S. Lang and J. Silverman. We complete the study with a comparison between differential lattice structures.
abelian varieties, Mathematics - Number Theory, 11G50, 14G40, 14G05, Heights, Theta heights, FOS: Mathematics, Rational points, Number Theory (math.NT), Arithmetic varieties and schemes; Arakelov theory; heights, Faltings heights, rational points
abelian varieties, Mathematics - Number Theory, 11G50, 14G40, 14G05, Heights, Theta heights, FOS: Mathematics, Rational points, Number Theory (math.NT), Arithmetic varieties and schemes; Arakelov theory; heights, Faltings heights, rational points
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