Some cases of Vojta’s conjecture on integral points over function fields

DOI10.1090/S1056-3911-07-00489-4zbMath1221.11146arXivmath/0512074WikidataQ123340526 ScholiaQ123340526MaRDI QIDQ5460230

Umberto Zannier, Pietro Corvaja

Publication date: 5 May 2008

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512074

zbMATH Keywords

\(S\)-units in function fieldslog Kodaira dimensioncomplement of a conic and two lines

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25)

Related Items (22)

An $abcd$ theorem over function fields and applications ⋮ Lang-Vojta conjecture over function fields for surfaces dominating \(\mathbb{G}_m^2\) ⋮ On some extensions of the Ailon-Rudnick theorem ⋮ Greatest common divisors of iterates of polynomials ⋮ On the Skolem problem and some related questions for parametric families of linear recurrence sequences ⋮ Greatest common divisors of \(u-1, v-1\) in positive characteristic and rational points on curves over finite fields ⋮ On fewnomials, integral points, and a toric version of Bertini’s theorem ⋮ Greatest common divisor results on semiabelian varieties and a conjecture of Silverman ⋮ A new unicity theorem and Erdös' problem for polarized semi-abelian varieties ⋮ Fibered threefolds and Lang-Vojta’s conjecture over function fields ⋮ A variant of a theorem by Ailon-Rudnick for elliptic curves ⋮ Greatest common divisors and Vojta's conjecture for blowups of algebraic tori ⋮ Hyperbolicity of Varieties of Log General Type ⋮ Nonspecial varieties and generalised Lang–Vojta conjectures ⋮ On Pisot's \(d\)-th root conjecture for function fields and related GCD estimates ⋮ Hilbert irreducibility above algebraic groups ⋮ On the \(d\)th roots of exponential polynomials and related problems arising from the Green-Griffiths-Lang conjecture ⋮ Two exponential Diophantine equations ⋮ On the exponential local-global principle for meromorphic functions and algebraic functions ⋮ Generalized greatest common divisors for orbits under rational functions ⋮ Intersections in subvarieties of ${\mathbb {G}}_{\mathrm {m}}^l$ and applications to lacunary polynomials ⋮ A cyclotomic generalization of the sequence \(\gcd(a^n-1, b^n-1)\)

Cites Work

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• Polynomial squares of the form \(aX^m+b(1-X)^n+c\)
• Diophantine approximations and value distribution theory
• Finiteness results for multiplicatively dependent points on complex curves
• An effective Schmidt's subspace theorem over function fields
• A lower bound for the height of a rational function at \(S\)-unit points
• Ternary form equations
• Degeneracy of holomorphic curves into algebraic varieties
• Generalized greatest common divisors, divisibility sequences, and Vojta's conjecture for blowups
• FEWNOMIALS AND INTERSECTIONS OF LINES WITH REAL ANALYTIC SUBGROUPS IN Gⁿ_m
• Vanishing sums in function fields
• Some Picard Theorems for Holomorphic Maps to Algebraic Varieties
• Rational curves on quasi-projective surfaces
• On the diophantine equation $f(a^m,y)=b^n$
• On the Functional Equation $f^2 = e^{2\phi_1} + e^{2\phi_2} + e^{2\phi_3} and a New Picard Theorem
• Torsion points on curves and common divisors of a^k-1 and b^k-1
• Some remarks on the S-unit equation in function fields

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