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The functor isn't right exact. For example,
$\mathrm{Ext}^1(A,\mathbb{G}_m)\simeq
H^1(A,\mathcal{O}_A^{\times})$$\mathrm{Ext}^1(A,\mathbb{G}_m)\simeq$
the set of primitive elements in $H^1(A,\mathcal{O}_A^{\times})$.
The functor isn't right exact. For example,
$\mathrm{Ext}^1(A,\mathbb{G}_m)\simeq
H^1(A,\mathcal{O}_A^{\times})$.
The functor isn't right exact. For example,
$\mathrm{Ext}^1(A,\mathbb{G}_m)\simeq$
the set of primitive elements in $H^1(A,\mathcal{O}_A^{\times})$.
