Fonctions Régulues

Abstract

We study the ring of rational functions admitting a continuous extension to the real affine space. We establish several properties of this ring. In particular, we prove a strong Nullstelensatz. We study the scheme theoretic properties and prove regulous versions of Theorems A and B of Cartan. We also give a geometrical characterization of prime ideals of this ring in terms of their zero-locus and relate them to euclidean closed Zariski-constructible sets.

In french. 49 pages, 6 figures, Journal für die reine und angewandte Mathematik (2014) To appear

References in corpus (2)

• The group of automorphisms of a real rational surface is n-transitive
• Geometrically rational real conic bundles and very transitive actions

Cited by in corpus (7)

• Curve-rational functions
• Some results of algebraic geometry over Henselian rank one valued fields
• Stratified-algebraic vector bundles
• A proof of Kurdyka's conjecture on arc-analytic functions
• Sums of even powers of k-regulous functions
• Extensions of arc-analytic functions
• Blown-up Čech cohomology and Cartan's Theorem B on real algebraic varieties