Let $C$ be an elliptic curve defined over $\mathbb{F}_p$. We know that the Frobenius morphism $\phi:C\longrightarrow C$ is inseparable, i.e, $K(C)/\phi^*K(C) = K(C)/K(C)^q$ is an inseparable extension.
How can I show that $1-\phi$ is separable?
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Sign up to join this communityLet $C$ be an elliptic curve defined over $\mathbb{F}_p$. We know that the Frobenius morphism $\phi:C\longrightarrow C$ is inseparable, i.e, $K(C)/\phi^*K(C) = K(C)/K(C)^q$ is an inseparable extension.
How can I show that $1-\phi$ is separable?