Ultrafilter and Constructible topologies on spaces of valuation domains

Carmelo A. Finocchiaro; Marco Fontana; K. Alan Loper

Ultrafilter and Constructible topologies on spaces of valuation domains

Commutative Algebra 2012-02-14 v1 Algebraic Geometry

Authors: Carmelo A. Finocchiaro , Marco Fontana , K. Alan Loper

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.

Keywords

valuation domains ultrafilter topology constructible topology Riemann-Zariski space spectral topologies commutative algebra

Cite

@article{arxiv.1202.2451,
  title  = {Ultrafilter and Constructible topologies on spaces of valuation domains},
  author = {Carmelo A. Finocchiaro and Marco Fontana and K. Alan Loper},
  journal= {arXiv preprint arXiv:1202.2451},
  year   = {2012}
}

Comments

Comm. Algebra (accepted for publication)

Ultrafilter and Constructible topologies on spaces of valuation domains

Abstract

Keywords

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