On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields

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dc.creatorWagner, Sven
dc.date2008-10-27
dc.date2009-02-25
dc.date.accessioned2026-07-07T12:46:04Z
dc.date.available2026-07-07T12:46:04Z
dc.descriptionWe 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.
dc.descriptionv2: Removed typos, changed content. v3: Added missing conditions for several results in section 6
dc.identifierhttps://arxiv.org/abs/0810.4800
dc.identifierhttp://arxiv.org/abs/0810.4800
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221259
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.titleOn the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields
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