On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields
Algebraic Geometry
2009-02-25 v3 Commutative Algebra
Abstract
We will prove that the Pierce-Birkhoff Conjecture holds for non-singular two-dimensional affine real algebraic varieties over real closed fields, i.e., if W is such a variety, then every piecewise polynomial function on W can be written as suprema of infima of polynomial functions on W. More precisely, we will give a proof of the so-called Connectedness Conjecture for the coordinate rings of such varieties, which implies the Pierce-Birkhoff Conjecture.
Cite
@article{arxiv.0810.4800,
title = {On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields},
author = {Sven Wagner},
journal= {arXiv preprint arXiv:0810.4800},
year = {2009}
}
Comments
v2: Removed typos, changed content. v3: Added missing conditions for several results in section 6