Uniform Bound for the Number of Rational Points on a Pencil of Curves

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Uniform Bound for the Number of Rational Points on a Pencil of Curves

JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)

ID	4527705
Author(s)	Dimitrov, Vesselin; Gao, Ziyang; Habegger, Philipp
Author(s) at UniBasel	Habegger, Philipp
Year	2019
Title	Uniform Bound for the Number of Rational Points on a Pencil of Curves
Journal	International mathematics research notices
Pages / Article-Number	rnz248
Abstract	Consider a one-parameter family of smooth, irreducible, projective curves of genus g≥2 defined over a number field. Each fiber contains at most finitely many rational points by the Mordell conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of the family and the Mordell–Weil rank of the fiber’s Jacobian. Our proof uses Vojta’s approach to the Mordell Conjecture furnished with a height inequality due to the 2nd- and 3rd-named authors. In addition we obtain uniform bounds for the number of torsion points in the Jacobian that lie in each fiber of the family.
Publisher	Hindawi Publ. Corp.
ISSN/ISBN	1073-7928
edoc-URL	https://edoc.unibas.ch/75076/
Full Text on edoc	No
Digital Object Identifier DOI	10.1093/imrn/rnz248

02/05/2024

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