An $abcd$ theorem over function fields and applications

DOI10.24033/bsmf.2613zbMath1252.11031OpenAlexW153117969MaRDI QIDQ2880697

Pietro Corvaja, Umberto Zannier

Publication date: 14 April 2012

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://smf4.emath.fr/en/Publications/Bulletin/139/html/smf_bull_139_437-454.php

zbMATH Keywords

function fieldsabc conjecturecurves on algebraic surfacesS-units

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Exponential Diophantine equations (11D61)

Related Items (4)

Greatest common divisors of \(u-1, v-1\) in positive characteristic and rational points on curves over finite fields ⋮ Analytic Ax-Schanuel for semi-abelian varieties and Nevanlinna theory ⋮ A variant of a theorem by Ailon-Rudnick for elliptic curves ⋮ Intersections in subvarieties of ${\mathbb {G}}_{\mathrm {m}}^l$ and applications to lacunary polynomials

Cites Work

• Vanishing sums in function fields
• Some remarks on the S-unit equation in function fields
• A POLYNOMIAL VARIANT OF A PROBLEM OF DIOPHANTUS FOR PURE POWERS
• Some cases of Vojta’s conjecture on integral points over function fields
• Higher-dimensional algebraic geometry
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