##  [Tate Module](/tate-module) 

  ##  [Tate Module](https://puremath.quantumdictionary.io/tate-module-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.