A 1-motive over a field $k$ is an algebraic torus $T$, an abelian variety $A$, a group scheme $G$ that's an extension of $A$ by $T$, a finitely generated free abelian group $L$, and a group homomorphism $L \longrightarrow G(k)$.

I'm currently reading a paper of Carlson, and I want to use his construction to identify something that came up in a problem that I'm working on. However, on the first page of that paper he defines a complex group scheme, but appears to leave out the requirement that $T$ and $G$ be group schemes. Later on (in section 4), he constructs the trace motive, and consistent with his definition, appears to only define the $\mathbb{C}$-points. I'm missing something -- but I don't really know what.

Does the fact that the groups in the trace motive come from group schemes somehow follow from some general nonsense about $\mathbb{C}$? Is it long and unenlightening to write down? Or am I just completely misunderstanding the paper?