Generalized Greatest Common Divisors, Divisibility Sequences, and Vojta's Conjecture for Blowups

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dc.creatorSilverman, Joseph H.
dc.date2004-07-26
dc.date2004-08-02
dc.date.accessioned2026-07-07T08:14:25Z
dc.date.available2026-07-07T08:14:25Z
dc.descriptionWe apply Vojta's conjecture to blowups and deduce a number of deep statements regarding (generalized) greatest common divisors on varieties, in particular on projective space and on abelian varieties. Special cases of these statements generalize earlier results and conjectures. We also discuss the relationship between generalized greatest common divisors and the divisibility sequences attached to algebraic groups, and we apply Vojta's conjecture to obtain a strong bound on the divisibility sequences attached to abelian varieties of dimension at least two.
dc.description20 pages; minor corrections (thanks to D. Abramovich, P. Corvaja, U. Zannier)
dc.identifierhttps://arxiv.org/abs/math/0407415
dc.identifierhttp://arxiv.org/abs/math/0407415
dc.identifierMonatsh. Math. 145 (2005), no. 4, 333--350. (MR2162351)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133114
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G35 (Primary); 11D75, 11J25, 14G25, 14J20 (Secondary)
dc.titleGeneralized Greatest Common Divisors, Divisibility Sequences, and Vojta's Conjecture for Blowups
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