= Internal Hom sheaf
{title2=$\mathcal Hom_{\mathcal O_X}(\mathcal F,\mathcal G)$}
For <sheaves of modules> $\mathcal F,\mathcal G$ on a <ringed space>, the internal Hom sheaf assigns to an open $U$ the module of <sheaf morphisms> $\mathcal F|_U\to\mathcal G|_U$ respecting $\mathcal O_U$. Compatible morphisms glue, so this is a sheaf. Its <global sections> are precisely the global module-sheaf morphisms. For a <locally free sheaf> $\mathcal F$ of finite rank it is $\mathcal F^\vee\otimes\mathcal G$.
Back to article page
