= Formal completion of a scheme
{title2=$X_{/Y}$}
For a <closed subscheme> with <ideal sheaf> $\mathcal I$ in a locally <Noetherian scheme>, the completion is the <formal scheme> on $|Y|$ with topological structure sheaf $\varprojlim_n(\mathcal O_X/\mathcal I^{n+1})|_{|Y|}$. On a Noetherian <affine scheme> $\operatorname{Spec}A$, it is $\operatorname{Spf}(\varprojlim_nA/I^{n+1})$. Its <adic topology> remembers every <infinitesimal neighbourhood>.
// Target: commutative-algebra.bigb
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