An extension of Greenberg's theorem to general valuation rings

DOI10.1007/S00229-011-0510-5zbMath1253.13011arXiv1106.0984OpenAlexW1982247462MaRDI QIDQ453353

Laurent Moret-Bailly

Publication date: 19 September 2012

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

Full work available at URL: https://arxiv.org/abs/1106.0984

zbMATH Keywords

valuation ringsordered groupsultraproductsclosed image mapclosed image theoremconvex subgroupsGreenberg's strong approximation theoremHenselian domaininfinitesimal Hasse principleschemes of finite presentation

Mathematics Subject Classification ID

Other nonalgebraically closed ground fields in algebraic geometry (14G27) Valuation rings (13F30) Étale and flat extensions; Henselization; Artin approximation (13B40) Ultraproducts and field theory (12L10)

Related Items (8)

Counter-examples to non-noetherian Elkik's approximation theorem ⋮ Decidability via the tilting correspondence ⋮ On the topology of relative and geometric orbits for actions of algebraic groups over complete fields ⋮ Artin approximation over Banach spaces ⋮ Approximation results of Artin-Tougeron-type for general filtrations and for \(C^r\)-equations ⋮ \(R\)-equivalence on families of rational varieties and the descent method ⋮ Artin-Mazur-Milne duality for fppf cohomology ⋮ Néron desingularization of extensions of valuation rings (with an appendix by Kęstutis Česnavičius)

Cites Work

• Ultraproducts and approximation in local rings. I
• Nombres de Tamagawa et groupes unipotents en caractéristique p
• The use of ultraproducts in commutative algebra
• Existential definability of non-nullity in rings
• Approximation properties for some non-Noetherian local rings
• Rational points in Henselian discrete valuation rings
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• Solutions d'équations à coefficients dans un anneau hensélien
• Unnamed Item

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