Premium
Nombre de points rationnels des courbes
Author(s) -
Rémond Gaël
Publication year - 2010
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdq005
Subject(s) - mathematics , integer (computer science) , rational number , jacobian matrix and determinant , degree (music) , polynomial , combinatorics , mathematical analysis , physics , computer science , acoustics , programming language
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 D 4 (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.