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 pipe 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 pipe A). We extend results regarding distinguished spectral topologies on spaces of valuation domains. © 2013 Copyright Taylor and Francis Group, LLC.
Ultrafilter and Constructible Topologies on Spaces of Valuation Domains
Finocchiaro C. A.;
2013-01-01
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 pipe 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 pipe A). We extend results regarding distinguished spectral topologies on spaces of valuation domains. © 2013 Copyright Taylor and Francis Group, LLC.File in questo prodotto:
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