Ihara's lemma

In mathematics, Ihara's lemma, introduced by Ihara (1975, lemma 3.2) and named by Ribet (1984), 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).