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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
moduli space
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gptkbp:alternativeName
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Shimura_variety
modular_variety
moduli_stack
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gptkbp:describes
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families of abelian varieties
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gptkbp:dimensions
|
can be higher-dimensional
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gptkbp:example
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gptkb:Siegel_modular_variety
modular group
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gptkbp:field
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gptkb:algebraic_geometry
|
|
gptkbp:firstDefined
|
1960s
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gptkbp:generalizes
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gptkb:Siegel_modular_variety
modular group
|
|
gptkbp:hasApplication
|
gptkb:Langlands_correspondence
study of L-functions
reciprocity laws
arithmetic of abelian varieties
proof of the modularity theorem
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|
gptkbp:hasLevelStructure
|
modular group
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gptkbp:hasSpecialCase
|
gptkb:Shimura_curve
gptkb:Mumford_curve
gptkb:Drinfeld_modular_variety
gptkb:Hilbert_modular_variety
gptkb:PEL-type_Shimura_variety
gptkb:Picard_modular_surface
Kuga variety
|
|
gptkbp:hasSpecialPoint
|
gptkb:CM_point
|
|
gptkbp:namedAfter
|
gptkb:Goro_Shimura
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|
gptkbp:originatedIn
|
quotients of symmetric spaces by arithmetic groups
|
|
gptkbp:referencedIn
|
gptkb:James_S._Milne,_Introduction_to_Shimura_Varieties
gptkb:Pierre_Deligne,_Travaux_de_Shimura
Goro Shimura, Introduction to the Arithmetic Theory of Automorphic Functions
|
|
gptkbp:relatedTo
|
gptkb:Langlands_program
modular forms
number theory
automorphic forms
modular group
moduli space
|
|
gptkbp:structure
|
gptkb:Hermitian_symmetric_domain
reductive algebraic group
|
|
gptkbp:studiedBy
|
gptkb:André_Weil
gptkb:Goro_Shimura
gptkb:Pierre_Deligne
|
|
gptkbp:studiedIn
|
number theory
|
|
gptkbp:usedIn
|
gptkb:Hodge_theory
representation theory
arithmetic geometry
motives
|
|
gptkbp:bfsParent
|
gptkb:algebraic_geometry
gptkb:superconformal_field_theory
gptkb:Algebraic_geometry
gptkb:Riemannian_manifold
gptkb:string_theory
gptkb:Seiberg–Witten_theory
gptkb:Yang-Mills_theory
gptkb:Kähler_manifold
gptkb:modular_group
gptkb:mirror_symmetry
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|
gptkbp:bfsLayer
|
5
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