Rational points on curves
Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 1, pp. 257-277.

This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009.

We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve C over . The focus is on practical aspects of this problem in the case that the genus of C is at least 2, and therefore the set of rational points is finite.

Ceci est la version longue de l’exposé invité que j’ai donné aux Journées Arithmétiques de St. Étienne en juillet 2009.

Nous discutons l’état de l’art pour le problème de trouver l’ensemble des points rationnels sur  d’une courbe C (projective lisse) géométriquement intègre. Nous nous concentrons sur les aspects pratiques de ce problème dans le cas où le genre de C est au moins 2, et par conséquent l’ensemble des points rationnels est fini.

DOI: 10.5802/jtnb.760
Classification: 11D41,  11G30,  14G05,  14G25
Michael Stoll 1

1 Mathematisches Institut Universität Bayreuth 95440 Bayreuth, Germany.
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Michael Stoll. Rational points on curves. Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 1, pp. 257-277. doi : 10.5802/jtnb.760. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.760/

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