On the density of rational and integral points on algebraic varieties

DOI10.1515/CRELLE.2007.037zbMath1130.14020arXivmath/0508326OpenAlexW2090579224MaRDI QIDQ5421662

Per Salberger

Publication date: 24 October 2007

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

Full work available at URL: https://arxiv.org/abs/math/0508326

zbMATH Keywords

upper boundrational pointscounting functionalgebraic varietybounded height

Mathematics Subject Classification ID

Rational points (14G05) Varieties over global fields (11G35)

Related Items (18)

On the density of integer points on generalised Markoff-Hurwitz and Dwork hypersurfaces ⋮ Density of rational points near/on compact manifolds with certain curvature conditions ⋮ Counting multiplicities in a hypersurface over a finite field ⋮ A generalization of the Bombieri-Pila determinant method ⋮ Counting rational points on projective varieties ⋮ On upper bounds of Manin type ⋮ On the global determinant method ⋮ Counting integral points of bounded height on varieties with large fundamental group ⋮ Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields ⋮ Uniform bounds for rational points on complete intersections of two quadric surfaces ⋮ The dimension growth conjecture, polynomial in the degree and without logarithmic factors ⋮ Rational points of bounded height on projective surfaces ⋮ Counting rational points on algebraic varieties ⋮ On the determinant method and geometric invariant theory ⋮ On the representation of \(k\)-free integers by binary forms ⋮ Complex cellular structures ⋮ Some counting questions for matrices with restricted entries ⋮ Uniform bounds for the number of rational points on varieties over global fields

Cites Work

• The density of rational points on non-singular hypersurfaces
• Varieties with many lines
• The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène).
• Counting rational points on algebraic varieties
• The number of integral points on arcs and ovals
• Counting Rational Points on Algebraic Varieties
• A Note on the Distribution of Rational Points on Threefolds
• THE DENSITY OF RATIONAL POINTS ON NON-SINGULAR HYPERSURFACES, I
• THE DENSITY OF RATIONAL POINTS ON NON-SINGULAR HYPERSURFACES, II

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