mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, Ihara's lemma, introduced by and named by , states that the kernel of the sum of the two ''p''-degeneracy maps from ''J''₀(''N'')×''J''₀(''N'') to ''J''₀(''Np'') is Eisenstein whenever the prime ''p'' does not divide ''N''. Here ''J''₀(''N'') is the

Jacobian In mathematics, a Jacobian, named for Carl Gustav Jacob Jacobi, may refer to: *Jacobian matrix and determinant *Jacobian elliptic functions *Jacobian variety *Intermediate Jacobian In mathematics, the intermediate Jacobian of a compact Kähler m ...

of the compactification of the modular curve of Γ₀(''N'').

References

* * Lemmas in number theory {{numtheory-stub