Year: 2013
Type: preprint
Abstract: This paper is concerned with algebraic geometry over complete discretely valued fields $K$ of equicharacteristic zero. Several results are given including: the canonical projection $K^{n} \times K\mathbb{P}^{m} \longrightarrow K^{n}$ and blow-ups of the $K$-points of smooth $K$-varieties are definably closed maps, a descent principle, a version of the Lojasiewicz inequality for continuous rational functions, curve selection for semialgebraic sets and the theorem on extending continuous hereditarily rational functions, established for the real field in our joint paper with J. Kollar. Our approach applies the quantifier elimination due to Pas. By the transfer principle of Ax-Kochen-Ershov, all these results carry over to the case of Henselian discretely valued fields. Using different arguments in our subsequent paper, we establish them over Henselian real valued fields of equicharacteristic zero.
Source: arXiv (Cornell University)
Author: Nowak, Krzysztof Jan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1855595192