= Stalk inclusion into rational sections of a locally free sheaf
{title2=$\mathcal F_P\hookrightarrow\operatorname{Rat}(\mathcal F)$}
On an <irreducible variety>, every nonempty <open subset> is dense, so a <germ> determines a <rational section>. For a <locally free sheaf>, this map is injective: a local section which vanishes on a dense open has all its regular coefficient functions zero, hence is zero. Local freeness is important; a section of a torsion sheaf can vanish generically without having zero <germ>.
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