Space of real arc germs and Poincaré series of a semi-algebraic set

DOI10.5802/aif.1814zbMath0967.14037OpenAlexW2330348033MaRDI QIDQ5928018

Ronan Quarez

Publication date: 20 March 2001

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2001__51_1_43_0

zbMATH Keywords

arc germPoincaré seriesquantifier eliminationreal constructible setsreal spectrumsemi-algebraic set

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Connections between field theory and logic (12L99) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Semialgebraic sets and related spaces (14P10) Germs of analytic sets, local parametrization (32B10)

Related Items (8)

Motivic-type invariants of blow-analytic equivalence. ⋮ A real nullstellensatz with multiplicity ⋮ On Grothendieck rings and algebraically constructible functions ⋮ On a motivic invariant of the arc-analytic equivalence ⋮ Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets ⋮ Virtual Betti numbers of real algebraic varieties. ⋮ Grothendieck ring of semialgebraic formulas and motivic real Milnor fibers ⋮ Complete classification of Brieskorn polynomials up to the arc-analytic equivalence

Cites Work

• Model theory.
• Germs of arcs on singular algebraic varieties and motivic integration
• Arc structure of singularities
• Uniform p-adic cell decomposition and local zeta functions.
• Fonction de Artin et Germes de Courbes Tracees sur un Germe D'Espace Analytique
• Courbes Tracees sur un Germe D'Hypersurface
• Rational points in Henselian discrete valuation rings
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