Rational solutions of certain equations involving norms

DOI10.1007/BF02392841zbMath1023.11033OpenAlexW2006066136WikidataQ57395855 ScholiaQ57395855MaRDI QIDQ1812468

D. R. Heath-Brown, Alexei N. Skorobogatov

Publication date: 11 November 2003

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392841

zbMATH Keywords

circle methodweak approximationHasse principletorsorBrauer-Manin obstructionprincipal homogeneous spacenorm form equationmethod of descentgeneric fibredensity of solutions

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Rational points (14G05) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25)

Related Items (16)

Progress concerning the local-global principle for zero-cycles on algebraic varieties ⋮ Rational solutions of certain Diophantine equations involving norms ⋮ On the equation N _{K /k} (Ξ)=P (t ) ⋮ Strong approximation and descent ⋮ Quadratic polynomials represented by norm forms ⋮ Principes locaux-globaux pour certaines fibrations en torseurs sous un tore ⋮ Schinzel hypothesis on average and rational points ⋮ Zéro-cycles sur les espaces homogènes et problème de Galois inverse ⋮ Norms as products of linear polynomials ⋮ The Hardy–Littlewood conjecture and rational points ⋮ The value of polynomials represented by norm forms ⋮ On the fibration method for zero-cycles and rational points ⋮ On Manin's conjecture for a family of Châtelet surfaces ⋮ Rational points on fibrations with few non-split fibres ⋮ Universal torsors and values of quadratic polynomials represented by norms ⋮ Optimal mean value estimates beyond Vinogradov's mean value theorem

Cites Work

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• La descente sur les variétés rationnelles. II. (The descent on rational varieties. II)
• Some remark on rational points
• The addition of norm forms
• Arithmetic on Some Singular Cubic Hypersurfaces
• Rational points and zero-cycles on fibred varieties: Schinzel's hypothesis and Salberger's device
• Descent on fibrations over P¹_k revisited
• Some Applications of the Local Uniformization Theorem

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