I am trying to read the article Théorie de Hodge II (which can be found in French here) and in page 24, when Deligne starts discussing Hodge structures, he makes the following claim about the character group of the torus $S=\mathrm{Res}_{\mathbb{C}/\mathbb{R}}(\mathbb{G}_m)$ (the multiplicative group on $\mathbb{C}$): $$ \mathrm{X}(S)=\mathrm{Hom}(S_\mathbb{C},\mathbb{G}_{m})=Hom(S,\mathbb{G}_m)(\mathbb{C}) $$ I understand that the first equality is just the definition and that multiplicative group on the middle is the multiplicative group over $\mathbb{C}$, whereas the one on the right is over $\mathbb{R}$. However, I don't get the notation $Hom(S,\mathbb{G}_m)(\mathbb{C})$, since $Hom(S,\mathbb{G}_m)$ is an abelian group. I have seen somewhere that this could mean tensor product with $\mathbb{C}$, but that doesn't fit with my intuition that the group $\mathrm{Hom}(S_\mathbb{C},\mathbb{G}_{m})$ should be free abelian of rank 2. Also, I don't get at all the sudden change to italic letters for the $\mathrm{Hom}$ (in case it is not a typo).
Thanks for any kind of help you may provide.