About: Functor represented by a scheme

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Functor represented by a scheme Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FFunctor_represented_by_a_scheme&invfp=IFP_OFF&sas=SAME_AS_OFF

In algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F. The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of .

Attributes	Values
rdf:type	Thing
rdfs:label	Functor represented by a scheme (en)
rdfs:comment	In algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F. The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of . (en)
rdfs:seeAlso	Rational point
dcterms:subject	Algebraic geometry
Wikipage page ID	45399927 (xsd:integer)
Wikipage revision ID	1107300373 (xsd:integer)
Link from a Wikipage to another Wikipage	Morphism of schemes Descent along torsors Algebraic topology Pseudo-functor Classifying space Function field (scheme theory) Stack (mathematics) Linear system of divisors Local ring Formal scheme Rational point Hilbert scheme Weil restriction Algebraic geometry Contravariant functor Scheme (mathematics) Yoneda lemma Residue field Representable functor Ring of dual numbers Fiber product Grothendieck site Yoneda's lemma dbr:Algebraizable dbr:Formal_solution
Link from a Wikipage to an external page	http://www.math.harvard.edu/~lurie/282ynotes/LectureXIV-Borel.pdf http://www.math.washington.edu/~zhang/Shanghai2011/Slides/ardakov.pdf
sameAs	Functor represented by a scheme Functor represented by a scheme
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Expand_section dbt:Reflist dbt:See_also dbt:Algebraic-geometry-stub
has abstract	In algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F. The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of . In some applications, it may not be possible to find a scheme that represents a given functor. This led to the notion of a stack, which is not quite a functor but can still be treated as if it were a geometric space. (A Hilbert scheme is a scheme, but not a stack because, very roughly speaking, deformation theory is simpler for closed schemes.) Some moduli problems are solved by giving (as opposed to polynomial algebraic solutions) and in that case, the resulting functor is represented by a formal scheme. Such a formal scheme is then said to be if there is another scheme that can represent the same functor, up to some isomorphisms. (en)
prov:wasDerivedFrom	wikipedia-en:Functor_represented_by_a_scheme?oldid=1107300373&ns=0
page length (characters) of wiki page	8123 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Functor_represented_by_a_scheme
is Link from a Wikipage to another Wikipage of	Rational point Ringed topos Functor of points
is Wikipage redirect of	Functor of points
is foaf:primaryTopic of	wikipedia-en:Functor_represented_by_a_scheme

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software