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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.".
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- Eisenstein_ideal wikiPageID "3772744".
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- Eisenstein_ideal wikiPageRevisionID "626848182".
- Eisenstein_ideal wikiPageWikiLink Atkin–Lehner_involution.
- Eisenstein_ideal wikiPageWikiLink Atkin–Lehner_theory.
- Eisenstein_ideal wikiPageWikiLink Category:Abelian_varieties.
- Eisenstein_ideal wikiPageWikiLink Category:Modular_forms.
- Eisenstein_ideal wikiPageWikiLink Correspondence_(mathematics).
- Eisenstein_ideal wikiPageWikiLink Divisor_class.
- Eisenstein_ideal wikiPageWikiLink Eisenstein_series.
- Eisenstein_ideal wikiPageWikiLink Endomorphism_ring.
- Eisenstein_ideal wikiPageWikiLink Fricke_involution.
- Eisenstein_ideal wikiPageWikiLink Ideal_(ring_theory).
- Eisenstein_ideal wikiPageWikiLink Jacobian_variety.
- Eisenstein_ideal wikiPageWikiLink Linear_system_of_divisors.
- Eisenstein_ideal wikiPageWikiLink Mathematics.
- Eisenstein_ideal wikiPageWikiLink Modular_curve.
- Eisenstein_ideal wikiPageWikiLink Publications_Mathxc3xa9matiques_de_lIHxc3x89S.
- Eisenstein_ideal wikiPageWikiLink Springer-Verlag.
- Eisenstein_ideal wikiPageWikiLink Springer_Science+Business_Media.
- Eisenstein_ideal wikiPageWikiLinkText "Eisenstein ideal".
- Eisenstein_ideal wikiPageWikiLinkText "Eisenstein".
- Eisenstein_ideal authorlink "Barry Mazur".
- Eisenstein_ideal first "Barry".
- Eisenstein_ideal hasPhotoCollection Eisenstein_ideal.
- Eisenstein_ideal last "Mazur".
- Eisenstein_ideal wikiPageUsesTemplate Template:Citation.
- Eisenstein_ideal wikiPageUsesTemplate Template:Harvs.
- Eisenstein_ideal year "1977".
- Eisenstein_ideal subject Category:Abelian_varieties.
- Eisenstein_ideal subject Category:Modular_forms.
- Eisenstein_ideal hypernym Ideal.
- Eisenstein_ideal type Group.
- Eisenstein_ideal type Group.
- Eisenstein_ideal type Variety.
- 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 Eisensteinideal.
- Eisenstein_ideal sameAs Q5349957.
- Eisenstein_ideal sameAs Q5349957.
- Eisenstein_ideal wasDerivedFrom Eisenstein_ideal?oldid=626848182.
- Eisenstein_ideal isPrimaryTopicOf Eisenstein_ideal.