= Tate module
{c}
{title2=$T_\ell(A)=\varprojlim_n A[\ell^n]$}
{wiki}
For an <abelian variety> $A$ and a <prime number> $\ell$ different from the characteristic, the inverse limit of its geometric $\ell^n$-torsion, with transition multiplication by $\ell$, is its Tate module. For an <elliptic curve>, it is free of rank two over the <p-adic integers> and satisfies $T_\ell(E)/\ell^nT_\ell(E)\simeq E[\ell^n]$. The <absolute Galois group> acts continuously and commutes with all base-defined <endomorphisms>.
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