Counting rational points on algebraic varieties

Journal article

For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant depends at most on d, ε, and N.

Authors: Browning, T; Heath-Brown, D; Salberger, P

• Publication status: Published
• Journal: DUKE MATHEMATICAL JOURNAL
• Volume: 132
• Issue: 3
• Pages: 545-578
• Publication date: 2006-04-15
• DOI: 10.1215/S0012-7094-06-13236-2
• ISSN: 0012-7094
• Language: English