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The key ingredient of this \"division theorem\" on freeness is the fact that, if $\\chi(\\mathcal{A}^H;t)$ divides $\\chi(\\mathcal{A};t)$, then the same holds for the localization at the codimension three flat in $H$. This implies the local-freeness of $\\mathcal{A}$ in codimension three along $H$. 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