English

Fonctions R\'egulues

Algebraic Geometry 2025-05-26 v4

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.

Keywords

Cite

@article{arxiv.1112.3800,
  title  = {Fonctions R\'egulues},
  author = {Goulwen Fichou and Johannes Huisman and Frédéric Mangolte and Jean-Philippe Monnier},
  journal= {arXiv preprint arXiv:1112.3800},
  year   = {2025}
}

Comments

In french. 49 pages, 6 figures, Journal f\"ur die reine und angewandte Mathematik (2014) To appear

R2 v1 2026-06-21T19:52:37.380Z