Mathematics – Commutative Algebra
Scientific paper
2012-02-11
Mathematics
Commutative Algebra
Comm. Algebra (accepted for publication)
Scientific paper
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.
Finocchiaro Carmelo A.
Fontana Marco
Loper Alan K.
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