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Complex multiplication

In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. 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.

Overview, Kronecker and abelian extensions & Sample consequence

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Overview

Example of the imaginary quadratic field extension

Abstract theory of endomorphisms

Kronecker and abelian extensions

Sample consequence

Singular moduli

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Map overview Semantic statistics

Complex multiplication

Nodes68
Edges67
Triples38
Avg. degree1.97
Density0.029412
Components1

How this topic connects Entity context

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Complex multiplication

Top relations

related to External links · 11
Complex multiplication → American Mathematical Society, Bulletin, Cite, CiteSeerX, Complex, Galois Representations, Kenneth, Modular Forms, October, PlanetMath, S2CID
related to Kronecker and abelian extensions · 11
Complex multiplication → Eisenstein, Gauss, Hilbert's, Indeed, Kronecker, Kronecker Jugendtraum, Let, Shimura's, Then, This, Weierstrass
related to Example of the imaginary quadratic field extension · 7
Complex multiplication → An, Consider, Conversely, Hilbert's, Kronecker, Kronecker Jugendtraum, To
related to Abstract theory of endomorphisms · 6
Complex multiplication → But, Frobenius, Hodge, It, The, When
is a · 2
Complex multiplication → exception, hardest to resolve for the Hodge conjecture
related to Singular moduli · 1
Complex multiplication → The

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Important terminology

complex elliptic multiplication theory field number quadratic abelian displaystyle imaginary integers curve ring algebraic curves endomorphisms integer functions also kronecker

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Complex multiplicationis aexception0.90text
Complex multiplicationis ahardest to resolve for the Hodge conjecture0.90text
Complex multiplicationrelated to Abstract theory of endomorphismsThe0.60section
Complex multiplicationrelated to Abstract theory of endomorphismsWhen0.60section
Complex multiplicationrelated to Abstract theory of endomorphismsFrobenius0.60section
Complex multiplicationrelated to Abstract theory of endomorphismsBut0.60section
Complex multiplicationrelated to Abstract theory of endomorphismsIt0.60section
Complex multiplicationrelated to Abstract theory of endomorphismsHodge0.60section
Complex multiplicationrelated to Example of the imaginary quadratic field extensionConsider0.60section
Complex multiplicationrelated to Example of the imaginary quadratic field extensionAn0.60section
Complex multiplicationrelated to Example of the imaginary quadratic field extensionConversely0.60section
Complex multiplicationrelated to Example of the imaginary quadratic field extensionKronecker0.60section

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