The Stacks project

Lemma 58.8.2. Let $(A, I)$ be a henselian pair. Set $X = \mathop{\mathrm{Spec}}(A)$ and $Z = \mathop{\mathrm{Spec}}(A/I)$. The functor

\[ \textit{FÉt}_ X \longrightarrow \textit{FÉt}_ Z,\quad U \longmapsto U \times _ X Z \]

is an equivalence of categories.

Proof. This is a translation of More on Algebra, Lemma 15.13.2. $\square$

Comments (2)

Comment #3036 by Brian Lawrence on

Suggested slogan: Finite etale covers lift uniquely to henselian rings.

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