Let $A$ be a semi-abelian variety over $K$, $\ell$ a prime number which is not equal to char($K$).

Does the abelianization of geometrically pro-$\ell$ etale fundamental group $(\pi_{1}(A\otimes\overline K)^{\ell})^{ab}$ isomorphic to the $\ell$-adic Tate module of $A$?


You probably know the answer is true for Abelian Varieties but I will post a reference here just for the record.


Section 10.37


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