Explicit uniform estimation of rational points II. Hypersurface coverings

DOI10.1515/CRELLE.2011.139zbMath1248.14031MaRDI QIDQ2904011

Huayi Chen

Publication date: 4 August 2012

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

zbMATH Keywords

number fieldsArakelov geometrycounting rational pointsdeterminant methodDiophantine geometrybounded heightslope method

Mathematics Subject Classification ID

Rational points (14G05) Counting solutions of Diophantine equations (11D45) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items

Counting multiplicities in a hypersurface over a finite field, Hilbert irreducibility, the Malle conjecture and the Grunwald problem, On the global determinant method, Counting integral points of bounded height on varieties with large fundamental group, On the determinant method and geometric invariant theory, Uniform bounds for the number of rational points on varieties over global fields

Cites Work

• Power-free values, large deviations, and integer points on irrational curves
• Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz
• The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène).
• Algebraic leaves of algebraic foliations over number fields.
• Rational points of bounded height on projective surfaces
• Counting rational points on algebraic varieties
• The number of integral points on arcs and ovals
• The Reduction Number of a One-Dimensional Local Ring
• Integral points on elliptic curves and 3-torsion in class groups
• THE DENSITY OF RATIONAL POINTS ON NON-SINGULAR HYPERSURFACES, I
• THE DENSITY OF RATIONAL POINTS ON NON-SINGULAR HYPERSURFACES, II
• Stable Ideals and Arf Rings