Ideal sheaf of a closed point
= Ideal sheaf of a closed point
{title2=$\mathcal I_P=\ker(\mathcal O_X\to k_P)$}
For a <closed point> $P$ with residue field $k(P)$, evaluation gives a morphism from the <structure sheaf> onto the <skyscraper sheaf> $k_P$. Its <kernel> is the ideal sheaf of $P$. On a <Noetherian scheme> it is a <coherent ideal sheaf>.