A note on a paper by R. Heath-Brown: The density of rational points on curves and surfaces

DOI10.1515/crll.2004.039zbMath1053.11027OpenAlexW1996500897MaRDI QIDQ4810854

Niklas Broberg

Publication date: 17 August 2004

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/9fb3051088b0db3557ebc2b841d057ac17cb35c2

zbMATH Keywords

Gröbner basesrational pointsprojective varietiesalgebraic curves and surfaces

Mathematics Subject Classification ID

Rational points (14G05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Counting solutions of Diophantine equations (11D45) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Varieties over global fields (11G35)

Related Items

Density of rational points near/on compact manifolds with certain curvature conditions ⋮ A generalization of the Bombieri-Pila determinant method ⋮ Hilbert irreducibility, the Malle conjecture and the Grunwald problem ⋮ Rational points on complete intersections over Fq(t)${\mathbb {F}}_q(t)$ ⋮ Counting rational points on projective varieties ⋮ On the global determinant method ⋮ Counting integral points of bounded height on varieties with large fundamental group ⋮ Uniform bounds for rational points on complete intersections of two quadric surfaces ⋮ Rational points of bounded height on projective surfaces ⋮ Counting rational points on hypersurfaces of low dimension ⋮ Counting rational points on algebraic varieties ⋮ On the determinant method and geometric invariant theory ⋮ Complex cellular structures ⋮ Uniform bounds for the number of rational points on varieties over global fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Number theory III: Diophantine geometry
• Diophantine approximations and diophantine equations
• The Geometry of Schemes
• What can be computed in algebraic geometry?