Fonctions régulues
-
Goulwen Fichou
,
Johannes Huisman
Abstract
Nous étudions l’anneau des fonctions rationnelles qui se prolongent
par continuité sur
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.
Funding statement: Ce travail a bénéficié d’un support partiel provenant du contrat ANR BirPol ANR-11-JS01-004-01.
Acknowledgements
Nous remercions J. Kollár pour nous avoir transmis une version préliminaire de son article, ainsi que S. Cantat, M. Coste, L. Evain, W. Kucharz, K. Kurdyka, D. Naie et A. Parusiński pour l’intérêt précoce qu’ils ont porté à nos travaux et pour leurs suggestions qui ont contribué à améliorer ce texte. Merci aussi à F. Broglia et F. Acquistapace pour nous avoir signalé les références [2, 1]. La version finale de cet article doit beaucoup au referee dont la lecture attentive et les remarques ont été très constructives.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Tight contact structures on the Brieskorn spheres -Σ(2,3,6n-1) and contact invariants
- Some examples of quasiisometries of nilpotent Lie groups
- Spans of special cycles of codimension less than 5
- The braided Thompson's groups are of type F∞
- Fonctions régulues
- A Dixmier--Douady theory for strongly self-absorbing C*-algebras
- Monodromy of A-hypergeometric functions
- Primitive ideals, twisting functors and star actions for classical Lie superalgebras
Artikel in diesem Heft
- Frontmatter
- Tight contact structures on the Brieskorn spheres -Σ(2,3,6n-1) and contact invariants
- Some examples of quasiisometries of nilpotent Lie groups
- Spans of special cycles of codimension less than 5
- The braided Thompson's groups are of type F∞
- Fonctions régulues
- A Dixmier--Douady theory for strongly self-absorbing C*-algebras
- Monodromy of A-hypergeometric functions
- Primitive ideals, twisting functors and star actions for classical Lie superalgebras
