Explicit uniform estimation of rational points I. Estimation of heights
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Publication:2904010
DOI10.1515/CRELLE.2011.138zbMath1249.14010OpenAlexW2070842170MaRDI QIDQ2904010
Publication date: 4 August 2012
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/crelle.2011.138
number fieldsArakelov geometrycounting rational pointsdeterminant methodDiophantine geometrybounded heightslope method
Rational points (14G05) Counting solutions of Diophantine equations (11D45) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)
Related Items (7)
Non-reduced fibers of an arithmetic scheme ⋮ Counting multiplicities in a hypersurface over a finite field ⋮ 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 ⋮ Control of the non-geometrically integral reductions
Cites Work
- Sur des hauteurs alternatives. I. (On alternative heights. I)
- Power-free values, large deviations, and integer points on irrational curves
- Sur des hauteurs alternatives. II (On alternative heights. II)
- 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 independence criteria.
- Formal groups and the isogeny theorem.
- Algebraic leaves of algebraic foliations over number fields.
- An arithmetic Riemann-Roch theorem
- Slopes of adelic vector bundles over global fields
- Rational points of bounded height on projective surfaces
- Counting rational points on algebraic varieties
- The number of integral points on arcs and ovals
- Zur algebraischen Geometrie. IX. Über zugeordnete Formen und algebraische Systeme von algebraischen Mannigfaltigkeiten
- Hermitian vector bundles and extension groups on arithmetic schemes. I: Geometry of numbers
- Riemann-Roch Type Inequalities
- Maximal slope of tensor product of Hermitian vector bundles
- Heights of Projective Varieties and Positive Green Forms
- Positive Line Bundles on Arithmetic Varieties
- 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
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