Free sheaf
= Free sheaf
{title2=$\mathcal O_X^{\oplus r}$}
A free sheaf of finite rank on a <scheme> is a <sheaf of modules> globally isomorphic to $\mathcal O_X^{\oplus r}$. A <locally free sheaf> only requires such an isomorphism on an open cover; its local frames need not glue to one global frame.