algebraic geometry - Locally on $D_+ (fg)$ the sheaves $\mathcal {O ...
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2 Yes. Recall (by Stacks 01M7, for instance) that Γ(D(fg),OX(nd)) = S(nd)(fg) Γ (D (f g), O X (n d)) = S (n d) (f g), the homogeneous localization at fg f g of the regular module shifted by nd n d, which is naturally a module over the ring S(fg) S (f g).
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