Weighted sums of squares in local rings and their completions. I

DOI10.1007/s00209-009-0551-6zbMath1198.14056OpenAlexW2109980502MaRDI QIDQ993358

Claus Scheiderer

Publication date: 10 September 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-009-0551-6

zbMATH Keywords

sums of squaresreal spectrumcompletionlocal ringssaturationpreorderingsreal algebraic geometrypositive polynomialsconstructible topologyspectral topologyexcellent ringArtin approximationcurve singularitiesKrull topologyhenselian ringbasic semialgebraic setslocal global principlesnonnegativity certificate

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Local complex singularities (32S05) Real algebraic and real-analytic geometry (14P99) Regular local rings (13H05) Étale and flat extensions; Henselization; Artin approximation (13B40) Excellent rings (13F40) Complete rings, completion (13J10)

Related Items (3)

A Positivstellensatz for projective real varieties ⋮ Semidefinite Representation for Convex Hulls of Real Algebraic Curves ⋮ Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings

Cites Work

• Positive semidefinite germs on the cone.
• Sums of two squares in analytic rings
• Sums of squares on real algebraic curves
• Spaces of orderings and abstract real spectra
• Sums of squares on real algebraic surfaces
• Algebraic approximation of structures over complete local rings
• Non-existence of degree bounds for weighted sums of squares representations
• On sums of squares in local rings
• Le théorème des zéros pour les variétés analytiques réelles de dimension $2$
• Sums of squares of regular functions on real algebraic varieties
• Sums of squares in real rings
• Sums of squares of linear forms
• Positive semidefinite germs in real analytic surfaces
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