The explicit Mordell Conjecture for families of curves (with an appendix by M. Stoll)

Checcoli, Sara and Veneziano, Francesco and Viada, Evelina. (2016) The explicit Mordell Conjecture for families of curves (with an appendix by M. Stoll). Cornell.

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Official URL: http://edoc.unibas.ch/40236/

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In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some explicit and sharp estimates for the height of such rational points, and the bounds are small enough to successfully implement a computer search. As an evidence of the simplicity of its application, we present a variety of explicit examples and explain how to produce many others. In the appendix our method is compared in detail to the classical method of Manin-Demjanenko and the analysis of our explicit examples is carried to conclusion.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Veneziano, Francesco
Item Type:Working Paper
Publisher:Cornell University Library
Number of Pages:42
Note:Publication type according to Uni Basel Research Database: Discussion paper / Internet publication
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Last Modified:27 Jun 2018 10:37
Deposited On:27 Jun 2018 10:37

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