Definition 63.3.10. If $x \in X(k)$ is a rational point and $\bar x : \mathop{\mathrm{Spec}}(\bar k) \to X$ the geometric point lying over $x$, we let $\pi _ x : \mathcal{F}_{\bar x} \to \mathcal{F}_{\bar x}$ denote the action by $\text{frob}_ k^{-1}$ and call it the geometric frobenius1

[1] This notation is not standard. This operator is denoted $F_ x$ in [SGA4.5]. We will likely change this notation in the future.

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