Counting rational points on algebraic varieties

Browning, T. D. ; Heath-Brown, D. R. ; Salberger, P.

Duke Math. J., Tome 131 (2006) no. 1, p. 545-578 / Harvested from Project Euclid

Résumé

For any $N \geq 2$ , let $Z \subset \mathbb{P}^N$ be a geometrically integral algebraic variety of degree $d$ . This article is concerned with the number $N_Z(B)$ of $\mathbb{Q}$ -rational points on $Z$ which have height at most $B$ . For any $\varepsilon>0$ , we establish the estimate $$N_Z(B)=O_{d,\varepsilon,N}(B^{\dim Z+\varepsilon})$$ , provided that $d \geq 6$ . As indicated, the implied constant depends at most on $d,\varepsilon$ , and $N$

Détail

Publié le : 2006-04-15
Classification:  14G05,  11G35