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Rational points on curves. (English. French summary) Zbl 1270.11030
Let $$C$$ be a geometrically integral algebraic curve defined over $${\mathbb Q}$$. The last fifteen year we have seen a great progress in the determination of the set of rational points of $$C$$. This paper discuss the state of the art of this problem. It mainly deals with curves of genus $$\geq 2$$ which have a finite set of rational points. The focus is on the computational aspects of this problem.

##### MSC:
 11D41 Higher degree equations; Fermat’s equation 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields 14G05 Rational points 14G25 Global ground fields in algebraic geometry
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