= Formal completion commutes with restriction to an open subscheme
{title2=$(X_{/Y})|_{U\cap Y}\cong U_{/(U\cap Y)}$}
Restricting the topological structure sheaf of a <formal completion of a scheme> to an <open subscheme> commutes with its <inverse limit>: both sheaves are $\varprojlim_n(\mathcal O_U/(\mathcal I|_U)^{n+1})$ on $|U\cap Y|$. Equivalently, the identical <infinitesimal neighbourhoods> have identical restricted structure sheaves. On formal affine charts this uses <completed localization of an adic ring>.
// Target: toric-geometry.bigb
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