Linear spaces on the intersection of cubic hypersurfaces

DOI10.1007/BF02349626zbMath0546.10018OpenAlexW2083109249MaRDI QIDQ798353

D. J. Lewis, Rainer Schulze-Pillot

Publication date: 1984

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178180

zbMATH Keywords

forms in many variablescubic formsBrauer inductioncommon p-adic solutionscommon zero setexistence of m-dimensional linear varietyupper bounds for number of variables

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Cubic and quartic Diophantine equations (11D25) (p)-adic theory (11E95)

Related Items (3)

HUA‐TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS ⋮ On the number of linear spaces on hypersurfaces with a prescribed discriminant ⋮ Rational linear spaces on hypersurfaces over quasi-algebraically closed fields

Cites Work

• On zeros of \(p\)-adic forms
• On \(p\)-adic zeros of forms
• The solubility of certain p-adic equations
• Diophantine inequalities for forms of odd degree
• On cubic polynomials. III: Systems of p-adic equations
• On cubic polynomials. IV: Systems of rational equations
• Systems of homogeneous equations
• Cubic homogeneous polynomials over \(\mathfrak p\)-adic number fields
• Homogeneous forms of odd degree in a large number of variables
• Cubic forms in sixteen variables
• Systems of quadratic forms.
• Simultaneous Quadratic Forms
• An Algebraic Proof of the Borsuk-Ulam Theorem for Polynomial Mappings
• Formes p-adiques anisotropes.
• Diophantine Problems Over Local Fields I
• Homogeneous additive equations
• A note on systems of homogeneous algebraic equations

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