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Lifting a Frobenius endomorphism under an étale morphism

^{n-r}_{\mathbb{F}_{p}}$ and hence a lift of this to $\mathbb{A}^{n-r}_{\mathbb{Z}/{p^2}}$ (this lift is not unique) and we have an étale morphism from $X$ to $\mathbb{A}^{n-r}_{\mathbb{Z}/{p^2}}$ by smoothness
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