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.
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