Rational equivalence on cubic hypersurfaces of bad reduction

DOI10.1016/j.jnt.2007.03.009zbMath1167.14007OpenAlexW2140628182MaRDI QIDQ958666

David A. Madore

Publication date: 5 December 2008

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2007.03.009

zbMATH Keywords

Chow groupscubic hypersurfaces\(p\)-adic fields\(R\)-equivalence

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Cubic and quartic Diophantine equations (11D25) Varieties over finite and local fields (11G25) Algebraic cycles (14C25) Hypersurfaces and algebraic geometry (14J70) (Equivariant) Chow groups and rings; motives (14C15)

Related Items (5)

𝑅-equivalence on low degree complete intersections ⋮ RATIONAL CURVES ON CUBIC HYPERSURFACES OVER FINITE FIELDS ⋮ A finiteness theorem for zero-cycles over \(p\)-adic fields ⋮ Lines on cubic hypersurfaces ⋮ Zero-cycles on diagonal cubic surfaces over \(p\)-adic fields

Cites Work

• Hilbert's theorem 90 for \(K^ 2\), with application to the Chow groups of rational surfaces
• Rationally connected varieties over finite fields
• Rational equivalence on cubic hypersurfaces on \(p\)-adic fields. (Équivalence rationnelle sur les hypersurfaces cubiques sur les corps \(p\) -adiques.)
• Specialization of zero cycles
• Cubic homogeneous polynomials over \(\mathfrak p\)-adic number fields
• On the Chow groups of certain rational surfaces
• Introduction to Toric Varieties. (AM-131)
• Le groupe de Chow d'une surface rationnelle sur un corps local
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