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arXiv · 1112.3800

Fonctions R\'egulues

Goulwen Fichou·Johannes Huisman·Frédéric Mangolte·Jean-Philippe Monnier
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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. 2011-12-16. Fonctions R\'egulues. https://doi.org/10.1515/crelle-2014-0034

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