Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:automorphismGroup |
gptkb:modular_group
|
| gptkbp:canBe |
compactified
|
| gptkbp:canBeDefinedOver |
rational numbers
|
| gptkbp:compact |
adding cusps
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:example |
X(N)
X_0(N) X_1(N) |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:genus |
depends on level N
|
| gptkbp:hasSubfield |
gptkb:algebraic_geometry
number theory |
| 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 gptkb:moduli_space gptkb:modular_function Hecke operators modular forms elliptic curves 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
|
| gptkbp:bfsLayer |
5
|
| http://www.w3.org/2000/01/rdf-schema#label |
modular curves
|