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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


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1435-5345
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Volume 2016, Issue 718

Issues

Fonctions régulues

Goulwen Fichou / Johannes Huisman
  • LMBA (UMR 6205), Université de Bretagne Occidentale, 6, Av. Victor Le Gorgeu, CS 93837, 29238 Brest Cedex 3, France
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/ Frédéric Mangolte / Jean-Philippe Monnier
Published Online: 2015-01-10 | DOI: https://doi.org/10.1515/crelle-2014-0034

Abstract

Nous étudions l’anneau des fonctions rationnelles qui se prolongent par continuité sur n. Nous établissons plusieurs propriétés algébriques de cet anneau dont un Nullstellensatz fort. Nous étudions les propriétés schématiques associées et montrons une version régulue des théorèmes A et B de Cartan. Nous caractérisons géométriquement les idéaux premiers de cet anneau à travers leurs lieux d’annulation et montrons que les fermés régulus coïncident avec les fermés algébriquement constructibles.

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 Nullstellensatz. 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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About the article

Received: 2013-05-09

Revised: 2014-03-16

Published Online: 2015-01-10

Published in Print: 2016-09-01


Ce travail a bénéficié d’un support partiel provenant du contrat ANR BirPol ANR-11-JS01-004-01.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 718, Pages 103–151, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0034.

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