Hyperbolic fibre spaces and Mordell's conjecture over function fields
type: Item
instance of: scholarly article
title: Hyperbolic fibre spaces and Mordell's conjecture over function fields
zbMATH Open document ID: 0583.32061
author: Junjiro Noguchi
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: \textit{S. Lang} [Bull. Am. Math. Soc., New Ser. 80, 779-787 (1974; Zbl 0298.14014)] discussed the higher dimensional analogue of Mordell's conjecture for curves of genus \(\geq 2\) in terms of hyperbolic manifolds and posed a relative formulation of the problem for algebraic families of hyperbolic varieties: If there are an infinite number of cross sections, then the family contains split subfamilies and almost all cross sections are due to constant ones. In this paper the author gives some affirmative answer to the above problem (main theorem). Then, assuming the conditions of the main theorem, he gives an analogue of Mordell's conjecture over function fields which was proved by \textit{J. I. Manin} [Izv. Akad. Nauk SSSR, Ser. Mat. 27, 1395-1440 (1963; Zbl 0166.169)] and \textit{H. Grauert} [Publ. Math., Inst. Hautes Étud. Sci. 25, 131-149 (1965; Zbl 0137.405)] who didn't assume these conditions.
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 3933483
zbMATH Keywords: hyperbolic fibre space
zbMATH Keywords: higher dimensional analogue of Mordell's conjecture for curves
zbMATH Keywords: hyperbolic manifolds
zbMATH Keywords: algebraic families of hyperbolic varieties
zbMATH Keywords: Mordell's conjecture over function fields
reviewed by: G. A. Soifer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195179839
OpenAlex ID: W2017986622
Wikidata QID: Q122980625
DOI: 10.2977/PRIMS/1195179839
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description: scientific article; zbMATH DE number 3933483