Definition 60.26.2. In Situation 60.26.1 an $F$-crystal on $X/S$ (relative to $\sigma$) is a pair $(\mathcal{E}, F_\mathcal {E})$ given by a crystal in finite locally free $\mathcal{O}_{X/S}$-modules $\mathcal{E}$ together with a map

$F_\mathcal {E} : (F_ X)_{\text{cris}}^*\mathcal{E} \longrightarrow \mathcal{E}$

An $F$-crystal is called nondegenerate if there exists an integer $i \geq 0$ a map $V : \mathcal{E} \to (F_ X)_{\text{cris}}^*\mathcal{E}$ such that $V \circ F_{\mathcal{E}} = p^ i \text{id}$.

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