= Infinitesimal neighbourhood of a closed subscheme
{title2=$X_n=V(\mathcal I^{n+1})$}
= Infinitesimal neighbourhoods of a closed subscheme
{synonym}
= Infinitesimal neighbourhood
{synonym}
For a <closed subscheme> defined by an <ideal sheaf> $\mathcal I$, its $n$th <infinitesimal neighbourhood> has structure sheaf $\mathcal O_X/\mathcal I^{n+1}$. All these neighbourhoods have the same underlying topological space because the radicals of $\mathcal I$ and its positive powers agree. Their <inverse limit> of structure sheaves is the <formal completion of a scheme>.
// Target: ringed-space.bigb
Back to article page
