Definition 29.48.1. Let $f : X \to S$ be a morphism of schemes. We say $f$ is finite locally free if $f$ is affine and $f_*\mathcal{O}_ X$ is a finite locally free $\mathcal{O}_ S$-module. In this case we say $f$ is has rank or degree $d$ if the sheaf $f_*\mathcal{O}_ X$ is finite locally free of degree $d$.
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