Lemmas in number theory

Ihara's lemma

In mathematics, Ihara's lemma, introduced by Ihara and named by , states that the kernel of the sum of the two p-degeneracy maps from J0(N)×J0(N) to J0(Np) is Eisenstein whenever the prime p does not divide N. Here J0(N) is the Jacobian of the compactification of the modular curve of Γ0(N). (Wikipedia).

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Jacobian variety | Modular curve | Mathematics | Eisenstein ideal