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- Moduli_scheme abstract "In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily solved by means of scheme theory alone, while others require some extension of the 'geometric object' concept (algebraic spaces, algebraic stacks of Michael Artin).Work of Grothendieck and David Mumford (see geometric invariant theory) opened up this area in the early 1960s. The more algebraic and abstract approach to moduli problems is to set them up as a representable functor question, then apply a criterion that singles out the representable functors for schemes. When this programmatic approach works, the result is a fine moduli scheme. Under the influence of more geometric ideas, it suffices to find a scheme that gives the correct geometric points. This is more like the classical idea that the moduli problem is to express the algebraic structure naturally coming with a set (say of isomorphism classes of elliptic curves). The result is then a coarse moduli scheme. Its lack of refinement is, roughly speaking, that it doesn't guarantee for families of objects what is inherent in the fine moduli scheme. As Mumford pointed out in his book Geometric Invariant Theory, one might want to have the fine version, but there is a technical issue (level structure and other 'markings') that must be addressed to get a question with a chance of having such an answer.".
- Moduli_scheme wikiPageID "3043915".
- Moduli_scheme wikiPageLength "1696".
- Moduli_scheme wikiPageOutDegree "18".
- Moduli_scheme wikiPageRevisionID "319458419".
- Moduli_scheme wikiPageWikiLink Alexander_Grothendieck.
- Moduli_scheme wikiPageWikiLink Algebraic_geometry.
- Moduli_scheme wikiPageWikiLink Algebraic_space.
- Moduli_scheme wikiPageWikiLink Category:Moduli_theory.
- Moduli_scheme wikiPageWikiLink Category:Representable_functors.
- Moduli_scheme wikiPageWikiLink David_Mumford.
- Moduli_scheme wikiPageWikiLink Elliptic_curve.
- Moduli_scheme wikiPageWikiLink Functor.
- Moduli_scheme wikiPageWikiLink Geometric_invariant_theory.
- Moduli_scheme wikiPageWikiLink Glossary_of_algebraic_geometry.
- Moduli_scheme wikiPageWikiLink Mathematics.
- Moduli_scheme wikiPageWikiLink Michael_Artin.
- Moduli_scheme wikiPageWikiLink Moduli_space.
- Moduli_scheme wikiPageWikiLink Representable_functor.
- Moduli_scheme wikiPageWikiLink Scheme_(mathematics).
- Moduli_scheme wikiPageWikiLink Stack_(mathematics).
- Moduli_scheme wikiPageWikiLinkText "Moduli scheme".
- Moduli_scheme wikiPageWikiLinkText "moduli scheme".
- Moduli_scheme id "m/m064510".
- Moduli_scheme title "Moduli theory".
- Moduli_scheme wikiPageUsesTemplate Template:Eom.
- Moduli_scheme wikiPageUsesTemplate Template:Math-stub.
- Moduli_scheme subject Category:Moduli_theory.
- Moduli_scheme subject Category:Representable_functors.
- Moduli_scheme hypernym Space.
- Moduli_scheme type Functor.
- Moduli_scheme comment "In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily solved by means of scheme theory alone, while others require some extension of the 'geometric object' concept (algebraic spaces, algebraic stacks of Michael Artin).Work of Grothendieck and David Mumford (see geometric invariant theory) opened up this area in the early 1960s.".
- Moduli_scheme label "Moduli scheme".
- Moduli_scheme sameAs Q6889799.
- Moduli_scheme sameAs m.08ms6m.
- Moduli_scheme sameAs Q6889799.
- Moduli_scheme wasDerivedFrom Moduli_scheme?oldid=319458419.
- Moduli_scheme isPrimaryTopicOf Moduli_scheme.