Abstract
The purpose of this paper is to prove, assuming that the conjecture of Lang and Vojta holds true, that there is a uniform bound on the number of stably integral points in the complement of the theta divisor on a principally polarized abelian surface defined over a number field. Most of our argument works in arbitrary dimension and the restriction on the dimension ≤2 is used only at the last step, where we apply Pacelli’s stronger uniformity results for elliptic curves.
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[ℵ95] D. Abramovich,Uniformité des points rationnels des courbes algébriques sur les extensions quadratiques et cubiques, Comptes Rendus de l’Académie des Sciences, Paris, Série I, Mathématique321 (1995), 755–758.
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Partially supported by NSF grant DMS-9700520 and by an Alfred P. Sloan research fellowship.
Partially supported by NSA grant MDA904-96-1-0008.
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Abramovich, D., Matsuki, K. Uniformity of stably integral points on principally polarized abelian varieties of dimension ≤2. Isr. J. Math. 121, 351–378 (2001). https://doi.org/10.1007/BF02802511
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DOI: https://doi.org/10.1007/BF02802511