Nombre de points rationnels des courbes

被引：11

作者：

Remond, Gael ^{[1
]}

机构：

[1] Inst Fourier, UMR 5582, F-38402 St Martin Dheres, France

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2010年 / 101卷

关键词：

BOUNDS; CASTELNUOVO;

D O I：

10.1112/plms/pdq005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F be a polynomial in two variables with integer coefficients, let D be its degree and let M >= 3 be an upper bound for the absolute value of its coefficients. Then the number of rational zeroes of F is either infinite or less than exp(5(D4) (log M)(log log M)). We prove this as a special case of a result for number fields. The main new ingredient is an estimate for the theta height of a Jacobian.

引用

页码：759 / 794

页数：36