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: http://www.math.uni-bielefeld.de/~mseverit/algkalgc.pdf page 2, 6th equation.

(cross post from http://math.stackexchange.com/questions/39186/quotient-category-coh-d-coh-d-1 )