= Locally free module
{title2=$P_{f_i}\cong A_{f_i}^r$}
A <locally free module> is one whose associated sheaf is locally a <free module>. In the finite constant-rank case, it becomes free of rank $r$ on a <principal open subset> cover of $\operatorname{Spec}A$. Equivalently it is a <finite projective module> of constant rank $r$. A surjection onto it splits, so the <kernel> is also finite projective. Its associated sheaf is a <locally free sheaf> and defines an algebraic <vector bundle>.
// Target: algebraic-geometry.bigb
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