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fppf

fidèlement plat de présentation finie, i.e. a flat morphism of finite presentation. An fppf covering is a covering \(T_i\to X\) by flat morphisms which are locally of finite presentation.

Needed in order to do Kummer theory for \(p{\hbox{-}}\)torsion in characteristic \(p\), since the following SES is exact in fppf sheaves but not in etale sheaves: \begin{align*} 0\to \mu_p \to {\mathbf{G}}_m \xrightarrow{\cdot p} {\mathbf{G}}_m\to 0 \end{align*}