Submission date: 8 November 2013.

Abstract:

This paper is concerned with algebraic geometry over complete discretely valued fields of equicharacteristic zero. Several results are given including: the canonical projection K^{n} \times O_m(K) ---> K^{n} and blow-ups along smooth centers of the K-points of smooth K-varieties are definably closed maps; a descent principle; the Lojasiewicz inequality for continuous rational functions; curve selection for semialgebraic sets and the theorem on extending continuous hereditarily rational functions, established in the case of locally compact fields in our joint paper with J. Kollár. Our approach applies the quantifier elimination due to Pas.

Mathematics Subject Classification:

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Full text arXiv 1311.2051: pdf, ps.