# Decomposition theorem for semi-abelian varieties

Fact :

• Let $B$ an abelian subvariety of an abelian variety over a field $K$. We know that there exist an abelian subvariety $C$ of $A$ such that the restriction of addition gives an isogeny $B\times_K C\to A$.

• The analogous result is true for an linear torus.

Questions :

1)Is this result is true in the category of semiabelians varieties ?

2)Is there a good reference on semi-abelians varieties ?

Thanks !