Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Modular_curve> ?p ?o }
- Modular_curve abstract "In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term modular curve can also be used to refer to the compactified modular curves X(Γ) which are compactifications obtained by adding finitely many points (called the cusps of Γ) to this quotient (via an action on the extended complex upper-half plane). The points of a modular curve parametrize isomorphism classes of elliptic curves, together with some additional structure depending on the group Γ. This interpretation allows one to give a purely algebraic definition of modular curves, without reference to complex numbers, and, moreover, prove that modular curves are defined either over the field Q of rational numbers, or a cyclotomic field. The latter fact and its generalizations are of fundamental importance in number theory.".
- Modular_curve wikiPageExternalLink m064410.htm.
- Modular_curve wikiPageID "669552".
- Modular_curve wikiPageLength "11417".
- Modular_curve wikiPageOutDegree "74".
- Modular_curve wikiPageRevisionID "657051793".
- Modular_curve wikiPageWikiLink Alexandroff_compactification.
- Modular_curve wikiPageWikiLink Alexandroff_extension.
- Modular_curve wikiPageWikiLink Algebraic_curve.
- Modular_curve wikiPageWikiLink Algebraic_geometry.
- Modular_curve wikiPageWikiLink Andrew_Ogg.
- Modular_curve wikiPageWikiLink Angular_defect.
- Modular_curve wikiPageWikiLink Arithmetic_geometry.
- Modular_curve wikiPageWikiLink Belyi_function.
- Modular_curve wikiPageWikiLink Belyis_theorem.
- Modular_curve wikiPageWikiLink Category:Algebraic_curves.
- Modular_curve wikiPageWikiLink Category:Modular_forms.
- Modular_curve wikiPageWikiLink Category:Riemann_surfaces.
- Modular_curve wikiPageWikiLink Centralizer_and_normalizer.
- Modular_curve wikiPageWikiLink Classical_modular_curve.
- Modular_curve wikiPageWikiLink Compact_space.
- Modular_curve wikiPageWikiLink Compactification_(mathematics).
- Modular_curve wikiPageWikiLink Complex_manifold.
- Modular_curve wikiPageWikiLink Congruence_subgroup.
- Modular_curve wikiPageWikiLink Coprime_integers.
- Modular_curve wikiPageWikiLink Correspondence_(mathematics).
- Modular_curve wikiPageWikiLink Cyclotomic_field.
- Modular_curve wikiPageWikiLink Defect_(geometry).
- Modular_curve wikiPageWikiLink Dessin_denfant.
- Modular_curve wikiPageWikiLink Dessins_denfants.
- Modular_curve wikiPageWikiLink Elliptic_curve.
- Modular_curve wikiPageWikiLink Elliptic_function.
- Modular_curve wikiPageWikiLink Euler_characteristic.
- Modular_curve wikiPageWikiLink Field_of_definition.
- Modular_curve wikiPageWikiLink Fractional_linear_transformation.
- Modular_curve wikiPageWikiLink Fuchsian_group.
- Modular_curve wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Modular_curve wikiPageWikiLink Gauss–Bonnet_theorem.
- Modular_curve wikiPageWikiLink Generalized_Kac–Moody_algebra.
- Modular_curve wikiPageWikiLink Genus_(mathematics).
- Modular_curve wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
- Modular_curve wikiPageWikiLink Group_action.
- Modular_curve wikiPageWikiLink Hecke_operator.
- Modular_curve wikiPageWikiLink Icosahedral_symmetry.
- Modular_curve wikiPageWikiLink Icosahedron.
- Modular_curve wikiPageWikiLink Irreducible_component.
- Modular_curve wikiPageWikiLink Irreducible_variety.
- Modular_curve wikiPageWikiLink J-invariant.
- Modular_curve wikiPageWikiLink Jack_Daniels.
- Modular_curve wikiPageWikiLink Jean-Pierre_Serre.
- Modular_curve wikiPageWikiLink John_G._Thompson.
- Modular_curve wikiPageWikiLink Klein_quartic.
- Modular_curve wikiPageWikiLink Linear_fractional_transformation.
- Modular_curve wikiPageWikiLink Manin–Drinfeld_theorem.
- Modular_curve wikiPageWikiLink Mazurs_torsion_theorem.
- Modular_curve wikiPageWikiLink Modular_arithmetic.
- Modular_curve wikiPageWikiLink Modular_equation.
- Modular_curve wikiPageWikiLink Modular_form.
- Modular_curve wikiPageWikiLink Modular_function.
- Modular_curve wikiPageWikiLink Modular_group.
- Modular_curve wikiPageWikiLink Modular_group_Gamma0.
- Modular_curve wikiPageWikiLink Modularity_theorem.
- Modular_curve wikiPageWikiLink Moduli_problem.
- Modular_curve wikiPageWikiLink Moduli_space.
- Modular_curve wikiPageWikiLink Monster_group.
- Modular_curve wikiPageWikiLink Monstrous_moonshine.
- Modular_curve wikiPageWikiLink Möbius_transformation.
- Modular_curve wikiPageWikiLink Noncompact.
- Modular_curve wikiPageWikiLink Normalizer.
- Modular_curve wikiPageWikiLink Number_theory.
- Modular_curve wikiPageWikiLink Orbit_(group_theory).
- Modular_curve wikiPageWikiLink PSL(2,7).
- Modular_curve wikiPageWikiLink Prime_number.
- Modular_curve wikiPageWikiLink Princeton_University_Press.
- Modular_curve wikiPageWikiLink Principal_congruence_subgroup.
- Modular_curve wikiPageWikiLink Quaternion_algebra.
- Modular_curve wikiPageWikiLink Quotient_by_a_group_action.
- Modular_curve wikiPageWikiLink Rational_number.
- Modular_curve wikiPageWikiLink Richard_Borcherds.
- Modular_curve wikiPageWikiLink Riemann_sphere.
- Modular_curve wikiPageWikiLink Riemann_surface.
- Modular_curve wikiPageWikiLink Riemann–Hurwitz_formula.
- Modular_curve wikiPageWikiLink Shimura_variety.
- Modular_curve wikiPageWikiLink Torsion_(algebra).
- Modular_curve wikiPageWikiLink Torsion_conjecture.
- Modular_curve wikiPageWikiLink Transcendental_function.
- Modular_curve wikiPageWikiLink Upper_half-plane.
- Modular_curve wikiPageWikiLinkText "Modular curve".
- Modular_curve wikiPageWikiLinkText "Modular curve#Genus zero".
- Modular_curve wikiPageWikiLinkText "modular curve".
- Modular_curve wikiPageWikiLinkText "modular curve".
- Modular_curve wikiPageWikiLinkText "modular".
- Modular_curve hasPhotoCollection Modular_curve.
- Modular_curve wikiPageUsesTemplate Template:Citation.
- Modular_curve wikiPageUsesTemplate Template:Refbegin.
- Modular_curve wikiPageUsesTemplate Template:Refend.
- Modular_curve wikiPageUsesTemplate Template:Reflist.
- Modular_curve wikiPageUsesTemplate Template:Unreferenced_section.
- Modular_curve subject Category:Algebraic_curves.
- Modular_curve subject Category:Modular_forms.