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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Compute $H^i(S,\underline{\text{Hom}}(A,\mathbb G_m))$ for a semi-abelian scheme $A$

How can I compute $H^i(S,\underline{\text{Hom}}(A,\mathbb G_m))$ (where $A$ denotes a semi-abelian scheme over $S$, $\mathbb G_m$ denotes the multiplicative group over $S$ and $\underline{\text{Hom}}$ …
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