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arXiv · 1202.2451

Ultrafilter and Constructible topologies on spaces of valuation domains

Carmelo A. Finocchiaro·Marco Fontana·K. Alan Loper
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Abstract

Let $K$ be a field and let $A$ be a subring of $K$. We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space Zar$(K|A)$ of all valuation domains having $K$ as quotient field and containing $A$. We show that the ultrafilter topology coincides with the constructible topology on the abstract Riemann-Zariski surface Zar$(K|A)$. We extend results regarding distinguished spectral topologies on spaces of valuation domains.

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Carmelo A. Finocchiaro, Marco Fontana, K. Alan Loper. 2012-02-11. Ultrafilter and Constructible topologies on spaces of valuation domains. https://arxiv.org/abs/1202.2451

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