About: Zariski–Riemann space

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In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve. Zariski–Riemann spaces were introduced by Zariski who (rather confusingly) called them Riemann manifolds or Riemann surfaces. They were named Zariski–Riemann spaces after Oscar Zariski and Bernhard Riemann by who used them to show that algebraic varieties can be embedded in complete ones.

Attributes	Values
rdf:type	Thing disease
rdfs:label	Zariski–Riemann space (en)
rdfs:comment	In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve. Zariski–Riemann spaces were introduced by Zariski who (rather confusingly) called them Riemann manifolds or Riemann surfaces. They were named Zariski–Riemann spaces after Oscar Zariski and Bernhard Riemann by who used them to show that algebraic varieties can be embedded in complete ones. (en)
dcterms:subject	Bernhard Riemann Algebraic geometry
Wikipage page ID	27902093 (xsd:integer)
Wikipage revision ID	1074298461 (xsd:integer)
Link from a Wikipage to another Wikipage	Bernhard Riemann Resolution of singularities Riemann surface Valuation ring Infinitely near point Bernhard Riemann Complete variety Local uniformization Algebraic geometry Field (mathematics) Oscar Zariski Germ (mathematics) Ring (mathematics) Algebraic geometry Bulletin of the AMS Springer-Verlag Locally ringed space
Link from a Wikipage to an external page	http://projecteuclid.org/euclid.kjm/1250524969
sameAs	Zariski–Riemann space Zariski–Riemann space Zariski–Riemann space
dbp:wikiPageUsesTemplate	dbt:Authority_control dbt:Citation dbt:Harvtxt dbt:Short_description dbt:Harvs
has abstract	In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve. Zariski–Riemann spaces were introduced by Zariski who (rather confusingly) called them Riemann manifolds or Riemann surfaces. They were named Zariski–Riemann spaces after Oscar Zariski and Bernhard Riemann by who used them to show that algebraic varieties can be embedded in complete ones. Local uniformization (proved in characteristic 0 by Zariski) can be interpreted as saying that the Zariski–Riemann space of a variety is nonsingular in some sense, so is a sort of rather weak resolution of singularities. This does not solve the problem of resolution of singularities because in dimensions greater than 1 the Zariski–Riemann space is not locally affine and in particular is not a scheme. (en)
gold:hypernym	Rings
prov:wasDerivedFrom	wikipedia-en:Zariski–Riemann_space?oldid=1074298461&ns=0
page length (characters) of wiki page	6148 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Zariski–Riemann_space
is Link from a Wikipage to another Wikipage of	Algebraic function field Resolution of singularities Glossary of algebraic geometry Local uniformization Algebraic variety Projective variety Riemann manifold Zariski space List of things named after Bernhard Riemann Nagata's compactification theorem Zariski-Riemann space Riemann-Zariski space Riemann-Zariski surface Riemann–Zariski space Zariski-Riemann surface Zariski Riemann surface Zariski–Riemann surface
is Wikipage redirect of	Zariski-Riemann space Riemann-Zariski space Riemann-Zariski surface Riemann–Zariski space Zariski-Riemann surface Zariski Riemann surface Zariski–Riemann surface
is foaf:primaryTopic of	wikipedia-en:Zariski–Riemann_space

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