Let $X$ be a scheme, and $Coh(X)_d$ be the category of coherent sheaves of support <= d dimensional.
Why is $Coh(X)_d/Coh(X)_{d-1}$ equivalent to $\oplus_{x \in X^{(d)}} \mathcal{A}(\mathcal{O}_{X,x})$?
See: http://www.math.uni-bielefeld.de/~mseverit/algkalgc.pdf page 2, 6th equation.