Integral points and Vojta’s conjecture on rational surfaces

DOI10.1090/S0002-9947-2011-05320-1zbMath1287.11091OpenAlexW2052040865WikidataQ122862678 ScholiaQ122862678MaRDI QIDQ3116573

Yu Yasufuku

Publication date: 24 February 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2011-05320-1

zbMATH Keywords

rational surfacesmultiplicative groupsintegral pointsgreatest common divisorsFarey sequencesVojta's conjectureblowups

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items

Greatest common divisors of integral points of numerically equivalent divisors ⋮ Divisibility of polynomials and degeneracy of integral points ⋮ Greatest common divisors and Vojta's conjecture for blowups of algebraic tori ⋮ Vojta's conjecture on rational surfaces and the \(abc\) conjecture ⋮ Vojta's conjecture on blowups of \({\mathbb{P}^n}\), greatest common divisors, and the \(abc\) conjecture

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Vojta's conjecture on blowups of \({\mathbb{P}^n}\), greatest common divisors, and the \(abc\) conjecture
• Diophantine approximation on abelian varieties
• Finiteness theorems for abelian varieties over number fields.
• Diophantine approximations and value distribution theory
• Linearformen mit algebraischen Koeffizienten
• On integral points on surfaces
• A lower bound for the height of a rational function at \(S\)-unit points
• Linear forms with algebraic coefficients. I
• Generalized greatest common divisors, divisibility sequences, and Vojta's conjecture for blowups
• Introduction to Toric Varieties. (AM-131)
• Vojta’s Main Conjecture for blowup surfaces