Geodesic
Counting Rational Points on Ruled Varieties
Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 264-270

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In this paper, we prove a general result computing the number of rational points of bounded height on a projective variety $V$ which is covered by lines. The main technical result used to achieve this is an upper bound on the number of rational points of bounded height on a line. This upper bound is such that it can be easily controlled as the line varies, and hence is used to sum the counting functions of the lines which cover the original variety $V$ .
DOI : 10.4153/CMB-2004-026-8
Mots-clés : 11G50, 11D45, 11D04, 14G05 
McKinnon, David. Counting Rational Points on Ruled Varieties. Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 264-270. doi: 10.4153/CMB-2004-026-8
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     author = {McKinnon, David},
     title = {Counting {Rational} {Points} on {Ruled} {Varieties}},
     journal = {Canadian mathematical bulletin},
     pages = {264--270},
     year = {2004},
     volume = {47},
     number = {2},
     doi = {10.4153/CMB-2004-026-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-026-8/}
}
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