no. 5
Rational points on a subanalytic surface
[Points rationnels d'une surface sous-analytique]
Pila, Jonathan1
1 McGill University, department of mathematics and statistics, Burnside Hall, 805 Sherbrooke Street West, Montreal, Quebec, H3A 2K6 (Canada), University of Oxford, mathematical institute, 24-29 St Giles, Oxford OX1 3LB (Grande-Bretagne)
Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1501-1516.

Soit X⊂ℝ n une surface sous-analytique compacte. Cet article démontre qu’en un sens convenable, il y a très peu de points rationnels de X qui ne se trouvent pas sur une courbe semi-algébrique connexe contenue dans X.

Let X⊂ℝ n be a compact subanalytic surface. This paper shows that, in a suitable sense, there are very few rational points of X that do not lie on some connected semialgebraic curve contained in X.

DOI : 10.5802/aif.2131
Classification : 11D99, 11J99
Keywords: Subanalytic set, rational point
Mot clés : ensemble sous-analytique, point rationnel
Pila, Jonathan 1

1 McGill University, department of mathematics and statistics, Burnside Hall, 805 Sherbrooke Street West, Montreal, Quebec, H3A 2K6 (Canada), University of Oxford, mathematical institute, 24-29 St Giles, Oxford OX1 3LB (Grande-Bretagne) 
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Pila, Jonathan. Rational points on a subanalytic surface. Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1501-1516. doi : 10.5802/aif.2131. http://www.numdam.org/articles/10.5802/aif.2131/

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