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arxiv: 1008.1905 · v1 · pith:ERGL7N42new · submitted 2010-08-11 · 🧮 math.NT · math.AG

Rational points on curves

classification 🧮 math.NT math.AG
keywords pointsrationalproblemarithmetiquesaspectscasecurvecurves
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This is an extended version of an invited lecture I gave at the Journees Arithmetiques in St. Etienne 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 Q. 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.

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