Abstract.
Faltings has proven the following conjecture of Lang: if A is an abelian variety over a number field and X any subvariety then all rational points of X lie on a finite number N of translates, contained in X, of abelian subvarieties of A. We provide an upper bound for N whose main feature is uniformity in X since it does not depend on the height of X. Moreover, the bound is completely explicit. Together with the result of a previous paper, the heart of the proof is a suitable generalization of Mumford’s theorem for curves.
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Oblatum 20-III-2000 & 3-V-2000¶Published online: 16 August 2000
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Rémond, G. Décompte dans une conjecture de Lang. Invent. math. 142, 513–545 (2000). https://doi.org/10.1007/s002220000095
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DOI: https://doi.org/10.1007/s002220000095