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  • Then if $x=\mathfrak{p} riangleleft A$, $\mathscr{F}_x\otimes_{\mathcal{O}_x}k(x) = M_\mathfrak{p}\otimes_{A_\mathfrak{p}}k(\mathfrak{p}) = M\otimes_A k(\mathfrak{p})$ is precisely the module presented by this matrix except with the entries interpreted as elements of $k(\mathfrak{p})$.
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