--- _id: '216' abstract: - lang: eng text: 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. author: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Roger full_name: Heath-Brown, Roger last_name: Heath Brown - first_name: Per full_name: Salberger, Per last_name: Salberger citation: ama: Browning TD, Heath Brown R, Salberger P. Counting rational points on algebraic varieties. Duke Mathematical Journal. 2006;132(3):545-578. doi:10.1215/S0012-7094-06-13236-2 apa: Browning, T. D., Heath Brown, R., & Salberger, P. (2006). Counting rational points on algebraic varieties. Duke Mathematical Journal. Unknown. https://doi.org/10.1215/S0012-7094-06-13236-2 chicago: Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational Points on Algebraic Varieties.” Duke Mathematical Journal. Unknown, 2006. https://doi.org/10.1215/S0012-7094-06-13236-2. ieee: T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points on algebraic varieties,” Duke Mathematical Journal, vol. 132, no. 3. Unknown, pp. 545–578, 2006. ista: Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on algebraic varieties. Duke Mathematical Journal. 132(3), 545–578. mla: Browning, Timothy D., et al. “Counting Rational Points on Algebraic Varieties.” Duke Mathematical Journal, vol. 132, no. 3, Unknown, 2006, pp. 545–78, doi:10.1215/S0012-7094-06-13236-2. short: T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132 (2006) 545–578. date_created: 2018-12-11T11:45:15Z date_published: 2006-04-15T00:00:00Z date_updated: 2021-01-12T06:55:41Z day: '15' doi: 10.1215/S0012-7094-06-13236-2 extern: 1 intvolume: ' 132' issue: '3' month: '04' page: 545 - 578 publication: Duke Mathematical Journal publication_status: published publisher: Unknown publist_id: '7696' quality_controlled: 0 status: public title: Counting rational points on algebraic varieties type: journal_article volume: 132 year: '2006' ...