Submission date: 10 December 2013.

Abstract:

This paper develops algebraic geometry over Henselian real valued fields K, being a sequel to our paper about that over Henselian discretely valued fields. Several results are given including: a version of curve selection for definable sets; the canonical projection K^n × KP^m → K^n and blow-ups of the K-points of smooth K-varieties are definably closed maps; a descent property for blow-ups; a version of the Lojasiewicz inequality for continuous rational functions and the theorem on extending continuous hereditarily rational functions, established in our joint paper with J. Kollar. The descent property enables application of desingularization and transformation to a normal crossing by blowing up in much the same way as over the locally compact ground field. Our approach applies quantifier elimination due to Pas.

Mathematics Subject Classification: Primary: 14G27, 03C10, Secondary: 12J25, 14P10

Keywords and phrases:

Full text arXiv 1312.2935: pdf, ps.