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- Complex_multiplication abstract "In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules). Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice. It has an aspect belonging to the theory of special functions, because such elliptic functions, or abelian functions of several complex variables, are then 'very special' functions satisfying extra identities and taking explicitly calculable special values at particular points. It has also turned out to be a central theme in algebraic number theory, allowing some features of the theory of cyclotomic fields to be carried over to wider areas of application.David Hilbert is said to have remarked that the theory of complex multiplication of elliptic curves was not only the most beautiful part of mathematics but of all science.".
- Complex_multiplication thumbnail Lattice_torsion_points.svg?width=300.
- Complex_multiplication wikiPageExternalLink ComplexMultiplication.html.
- Complex_multiplication wikiPageExternalLink ExamplesOfEllipticCurvesWithComplexMultiplication.html.
- Complex_multiplication wikiPageID "537183".
- Complex_multiplication wikiPageRevisionID "606732721".
- Complex_multiplication hasPhotoCollection Complex_multiplication.
- Complex_multiplication subject Category:Abelian_varieties.
- Complex_multiplication subject Category:Class_field_theory.
- Complex_multiplication subject Category:Elliptic_functions.
- Complex_multiplication type AbelianVarieties.
- Complex_multiplication type Abstraction100002137.
- Complex_multiplication type Assortment108398773.
- Complex_multiplication type Collection107951464.
- Complex_multiplication type EllipticFunctions.
- Complex_multiplication type Function113783816.
- Complex_multiplication type Group100031264.
- Complex_multiplication type MathematicalRelation113783581.
- Complex_multiplication type Relation100031921.
- Complex_multiplication comment "In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules).".
- Complex_multiplication label "Complex multiplication".
- Complex_multiplication label "Complexe vermenigvuldiging".
- Complex_multiplication label "Moltiplicazione complessa".
- Complex_multiplication label "Multiplication complexe".
- Complex_multiplication label "Multiplicação complexa".
- Complex_multiplication label "虚数乗法".
- Complex_multiplication sameAs Multiplication_complexe.
- Complex_multiplication sameAs Moltiplicazione_complessa.
- Complex_multiplication sameAs 虚数乗法.
- Complex_multiplication sameAs 복소_곱셈.
- Complex_multiplication sameAs Complexe_vermenigvuldiging.
- Complex_multiplication sameAs Multiplicação_complexa.
- Complex_multiplication sameAs m.02mtmb.
- Complex_multiplication sameAs Q2654923.
- Complex_multiplication sameAs Q2654923.
- Complex_multiplication sameAs Complex_multiplication.
- Complex_multiplication wasDerivedFrom Complex_multiplication?oldid=606732721.
- Complex_multiplication depiction Lattice_torsion_points.svg.
- Complex_multiplication isPrimaryTopicOf Complex_multiplication.