Let $j:Y \to X$ be a closed embedding of schemes.
Then we know there is an exact sequence in the Zariski topology
$0 \to I \to \mathcal{O}_X \to j_{*} \mathcal{O}_Y \to 0$.
Now consider the sheaf $\mathbb{G}_a$ in the fppf topology.
Does there exist a similar exact sequence in the fppf topology?
$0 \to I \to \mathbb{G}_a \to j_{*} \mathbb{G}_a \to 0$.
If yes, how do we describe the sheaf $I$ in this case? Is it quasicoherent?