Fonctions Régulues

Goulwen Fichou (1) , Johannes Huisman (2) , Frédéric Mangolte (3) , Jean-Philippe Monnier (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LM - Laboratoire de mathématiques de Brest
3 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Mots clés: regular function; regulous function; rational function; real algebraic variety

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou, Johannes Huisman, Frédéric Mangolte, Jean-Philippe Monnier. Fonctions Régulues. Journal für die reine und angewandte Mathematik, 2016, 718 (718), pp.103-151. ⟨10.1515/crelle-2014-0034⟩. ⟨hal-00652828v4⟩