4
$\begingroup$

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 $A$?

$\endgroup$
0

1 Answer 1

3
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.