Uniformity of stably integral points on principally polarized abelian surfaces

dc.creatorAbramovich, Dan
dc.creatorMatsuki, Kenji
dc.date1998-09-05
dc.date.accessioned2026-07-07T05:25:53Z
dc.date.available2026-07-07T05:25:53Z
dc.descriptionWe 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. This gives a uniform version, in the spirit of a result of Caporaso-Harris-Mazur, of an unconditional theorem of Faltings. We utilize recent results of Alexeev and Nakamura on complete moduli for quasi-abelian varieties. We expect that a thorough understanding of current work of Alexeev should give a more general result for abelian varieties of an arbitrary dimension with a polarizing divisor of an arbitrary degree - a proposed approach for such a generalization is given at the end of the paper.
dc.descriptionLatex 2e, 21 pages
dc.identifierhttps://arxiv.org/abs/math/9809023
dc.identifierhttp://arxiv.org/abs/math/9809023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77355
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14G05, 14K10, 11G10
dc.titleUniformity of stably integral points on principally polarized abelian surfaces
dc.typetext

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