Ultrafilter and Constructible topologies on spaces of valuation domains

2012/02/11 by Carmelo Antonio Finocchiaro, Finocchiaro, Carmelo A., Marco Fontana +3
Mathematics · #13A18 #13F05 #13G05 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1202.2451

openalex publication_date 2012/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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