The Zariski-Riemann Space of Valuation Rings

Bruce Olberding ()
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Bruce Olberding: New Mexico State University, Department of Mathematical Sciences

A chapter in Commutative Algebra, 2021, pp 639-667 from Springer

Abstract: Abstract Let F be a field, and let k be a subring of F. The Zariski-Riemann space X $${\mathcal X}$$ of F∕k is the set of valuation rings of F∕k endowed with the Zariski topology. With a sheaf of rings defined in a natural way, Zar ( F ∕ k ) $$\operatorname {Zar}(F/k)$$ is a locally ringed space. We discuss topological and geometric features of this space, as well as applications that illustrate these features.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_21

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DOI: 10.1007/978-3-030-89694-2_21

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