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no. S1
On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields
Sven Wagner1
1 Universität Konstanz Fachbereich Mathematik und Statistik 78457 Konstanz, Germany
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. S1, pp. 221-242.

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.

DOI: 10.5802/afst.1283

Sven Wagner 1

1 Universität Konstanz Fachbereich Mathematik und Statistik 78457 Konstanz, Germany 
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     title = {On the {Pierce-Birkhoff} {Conjecture} for {Smooth} {Affine} {Surfaces} over {Real} {Closed} {Fields}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
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Sven Wagner. On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. S1, pp. 221-242. doi : 10.5802/afst.1283. https://afst.centre-mersenne.org/articles/10.5802/afst.1283/

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