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- Eisenstein_ideal abstract "In mathematics, the Eisenstein ideal is an ideal in the endomorphism ring of the Jacobian variety of a modular curve, consisting roughly of elements of the Hecke algebra that annihilate the Eisenstein series. It was introduced by Barry Mazur (1977), in studying the rational points of modular curves. An Eisenstein prime is a prime in the support of the Eisenstein ideal (this has nothing to do with primes in the Eisenstein integers). Let N be a rational prime, and defineJ0(N) = Jas the Jacobian variety of the modular curve X0(N) = X.There are endomorphisms Tl of J for each prime number l not dividing N. These come from the Hecke operator, considered first as an algebraic correspondence on X, and from there as acting on divisor classes, which gives the action on J. There is also a Fricke involution w (and Atkin–Lehner involutions if N is composite). The Eisenstein ideal, in the (unital) subring of End(J) generated as a ring by the Tl, is generated as an ideal by the elements Tl − l - 1for all l not dividing N, and byw + 1.".
- Eisenstein_ideal wikiPageExternalLink item?id=PMIHES_1977__47__33_0.
- Eisenstein_ideal wikiPageExternalLink item?id=SB_1974-1975__17__238_0.
- Eisenstein_ideal wikiPageID "3772744".
- Eisenstein_ideal wikiPageRevisionID "522864731".
- Eisenstein_ideal authorlink "Barry Mazur".
- Eisenstein_ideal first "Barry".
- Eisenstein_ideal hasPhotoCollection Eisenstein_ideal.
- Eisenstein_ideal last "Mazur".
- Eisenstein_ideal year "1977".
- Eisenstein_ideal subject Category:Abelian_varieties.
- Eisenstein_ideal subject Category:Modular_forms.
- Eisenstein_ideal type AbelianVarieties.
- Eisenstein_ideal type Abstraction100002137.
- Eisenstein_ideal type Assortment108398773.
- Eisenstein_ideal type Collection107951464.
- Eisenstein_ideal type Form106290637.
- Eisenstein_ideal type Group100031264.
- Eisenstein_ideal type LanguageUnit106284225.
- Eisenstein_ideal type ModularForms.
- Eisenstein_ideal type Part113809207.
- Eisenstein_ideal type Relation100031921.
- Eisenstein_ideal type Word106286395.
- Eisenstein_ideal comment "In mathematics, the Eisenstein ideal is an ideal in the endomorphism ring of the Jacobian variety of a modular curve, consisting roughly of elements of the Hecke algebra that annihilate the Eisenstein series. It was introduced by Barry Mazur (1977), in studying the rational points of modular curves. An Eisenstein prime is a prime in the support of the Eisenstein ideal (this has nothing to do with primes in the Eisenstein integers).".
- Eisenstein_ideal label "Eisenstein ideal".
- Eisenstein_ideal sameAs m.09_68d.
- Eisenstein_ideal sameAs Q5349957.
- Eisenstein_ideal sameAs Q5349957.
- Eisenstein_ideal sameAs Eisenstein_ideal.
- Eisenstein_ideal wasDerivedFrom Eisenstein_ideal?oldid=522864731.
- Eisenstein_ideal isPrimaryTopicOf Eisenstein_ideal.