A higher dimensional analogue of Mordell's conjecture over function fields

DOI10.1007/BF01450536zbMath0459.14002WikidataQ122979584 ScholiaQ122979584MaRDI QIDQ1151939

Junjiro Noguchi

Publication date: 1981

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163589

zbMATH Keywords

Mordell's conjecture over function fieldsset of K-rational points

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Rational points (14G05) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (15)

Arithmetic on curves ⋮ Ampleness of intersections of translates of theta divisors in an abelian fourfold ⋮ The Mordell-Bombieri-Noguchi conjecture over function fields ⋮ The Mordell property of hyperbolic fiber spaces with noncompact fibers ⋮ Hyperbolic and Diophantine analysis ⋮ Rational points of varieties with ample cotangent bundle over function fields ⋮ Questions of decidability and undecidability in Number Theory ⋮ Sequences of powers with second differences equal to two and hyperbolicity ⋮ Hyperbolicity of Varieties of Log General Type ⋮ Nonspecial varieties and generalised Lang–Vojta conjectures ⋮ Examples of geometric Bombieri-Lang-Noguchi outside Mordell-Lang: nonrigid varieties with ample but not globally generated cotangent bundle ⋮ Recent results on the Kobayashi and Green-Griffiths-Lang conjectures ⋮ Rational points on quartics ⋮ Quadratic sequences of powers and Mohanty’s conjecture ⋮ Unnamed Item

Cites Work

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• Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper
• On Mordell's conjecture for algebraic curves over function fields
• Complements à un article de Hans Grauert sur la conjecture de Mordell
• Lectures on old and new results on algebraic curves
• Ample vector bundles
• Finiteness of the Family of Rational and Meromorphic Mappings Into Algebraic Varieties
• Higher dimensional diophantine problems
• Negative Vector Bundles and Complex Finsler Structures
• Holomorphic mappings into a compact quotient of symmetric bounded domain

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