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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 $A$?

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1 Answer 1

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

http://staff.science.uva.nl/~bmoonen/boek/TateBT.pdf

Section 10.37

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