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Let $X$ be a regular scheme, and $Coh(X)_d$ be the category of coherent sheaves of $\leq d$ dimensional support.

Why is $Coh(X)_d/Coh(X)_{d-1}$ equivalent to $\bigoplus_{x \in X_d} \mathcal{A}(\mathcal{O}_{X,x})$?

See: page 2, 6th equation.

(cross post from )

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