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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:automorphismGroup
|
modular group
|
|
gptkbp:canBe
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compactified
|
|
gptkbp:canBeDefinedOver
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rational numbers
|
|
gptkbp:compact
|
adding cusps
|
|
gptkbp:definedIn
|
complex numbers
|
|
gptkbp:example
|
X(N)
X_0(N)
X_1(N)
|
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gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:genus
|
depends on level N
|
|
gptkbp:hasSubfield
|
gptkb:algebraic_geometry
number theory
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
modular curves
|
|
gptkbp:isQuotientOf
|
upper half-plane by congruence subgroup
|
|
gptkbp:parameterize
|
isomorphism classes of elliptic curves with level structure
|
|
gptkbp:relatedTo
|
gptkb:modular_abelian_varieties
gptkb:modularity_theorem
Hecke operators
modular forms
elliptic curves
moduli space
modular function
Galois representations
Jacobians of modular curves
|
|
gptkbp:studiedBy
|
gptkb:Yutaka_Taniyama
gptkb:André_Weil
gptkb:Jean-Pierre_Serre
gptkb:Goro_Shimura
|
|
gptkbp:usedIn
|
proof of Fermat's Last Theorem
|
|
gptkbp:bfsParent
|
gptkb:Klein_quartic
gptkb:Langlands_correspondence
gptkb:modular_group
gptkb:Algebraic_number_theory
gptkb:Eisenstein_ideal
|
|
gptkbp:bfsLayer
|
5
|