Tate Module

For a prime ℓ and an algebraic group such as an abelian variety A, the Tate module T_ℓ(A) is the inverse limit of the ℓ^n‑torsion subgroups A[ℓ^n] under multiplication maps, producing a free Z_ℓ‑module of finite rank equipped with a continuous action of the absolute Galois group.