Lemma 52.24.2. In Situation 52.16.1 assume

$I = (f)$ is principal,

$A$ is $f$-adically complete,

$f$ is a nonzerodivisor,

$H^1_\mathfrak a(A/fA)$ and $H^2_\mathfrak a(A/fA)$ are finite $A$-modules.

Then with $U_0 = U \cap V(f)$ the completion functor

is an equivalence on the full subcategories of finite locally free objects.

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