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

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