Lemma 58.20.2. Let (A, \mathfrak m) be a Noetherian local ring. Set X = \mathop{\mathrm{Spec}}(A) and let U = X \setminus \{ \mathfrak m\} . Let V be finite étale over U. Assume A has depth \geq 2. The following are equivalent
V = Y \times _ X U for some Y \to X finite étale,
B = \Gamma (V, \mathcal{O}_ V) is finite étale over A.
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