The Stacks project

Definition 33.36.1. Let $p$ be a prime number. Let $X$ be a scheme in characteristic $p$. The absolute frobenius of $X$ is the morphism $F_ X : X \to X$ given by the identity on the underlying topological space and with $F_ X^\sharp : \mathcal{O}_ X \to \mathcal{O}_ X$ given by $g \mapsto g^ p$.