Tate module
In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made in the following situation: G is a commutative group scheme over a field K, Ks is the separable closure of K, and A = G(Ks) (the Ks-valued points of G). In this case, the Tate module of A is equipped with an action of the absolute Galois group of K, and it is referred to as the Tate module of G. == Definition == Given an abelian group A and a prime number p, the p-adic Tate module of A is T p ( A ) = lim ⟵ A [ p n ] {\displaystyle T_{p}(A)={\underset {\longleftarrow }{\lim }}A[p^{n}]} where A[pn] is the pn torsion of A (i.e.