Remark 59.23.4. In the terminology introduced above a special case of Theorem 59.22.4 is

$H_{fppf}^ p(X, \mathbf{G}_ a) = H_{\acute{e}tale}^ p(X, \mathbf{G}_ a) = H_{Zar}^ p(X, \mathbf{G}_ a) = H^ p(X, \mathcal{O}_ X)$

for all $p \geq 0$. Moreover, we could use the notation $H^ p_{fppf}(X, \mathcal{O}_ X)$ to indicate the cohomology of the structure sheaf on the big fppf site of $X$.

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