let $A$ be an abelian variety and $T$ be an algebraic torus over a field $k$; furthermore denote with $\mathbb G_a$ the additive group over $k$, i.e. just the affine space.
Why does then hold
(i) $Hom(T, \mathbb G_a)=0$
(ii) $Hom(A, \mathbb G_a)=0$
(iii) $Ext^1(T, \mathbb G_a)=0$,
if the hom groups denote really homomorphisms of group schemes?