Integral points on curves: Siegel’s theorem after Siegel’s proof View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2014

AUTHORS

Clemens Fuchs , Umberto Zannier

ABSTRACT

In this article, conceived as an addendum of comments to the present translation of Siegel’s paper, we shall present (in brief form) some fairly modern arguments for Siegel’s theorem on integral points on curves, appearing in the second part of his paper [48] that is translated here; we shall refer to the more modern statement appearing as Theorem 3.2 below. The arguments presented here appeared after the original proof. All of these proofs rely on Diophantine Approximation and use suitable versions of Roth’s theorem (1955) or Schmidt’s Subspace Theorem (about 1970). Siegel had not Roth’s theorem [45], which led to considerable complications in his proof. Some of the arguments below may be considered versions of Siegel’s one, simplified both by the use of Roth’s theorem and also by geometrical results on abelian varieties.1 More... »

PAGES

139-157

Book

TITLE

On Some Applications of Diophantine Approximations

ISBN

978-88-7642-519-6
978-88-7642-520-2

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-88-7642-520-2_3

DOI

http://dx.doi.org/10.1007/978-88-7642-520-2_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035206011


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