Quotient category $Coh(X)_d/Coh(X)_{d-1}$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T09:22:50Z http://mathoverflow.net/feeds/question/65044 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65044/quotient-category-cohx-d-cohx-d-1 Quotient category $Coh(X)_d/Coh(X)_{d-1}$ unknown (google) 2011-05-15T15:16:48Z 2011-05-15T15:16:48Z <p>Let $X$ be a regular scheme, and $Coh(X)_d$ be the category of coherent sheaves of $\leq d$ dimensional support.</p> <p>Why is <code>$Coh(X)_d/Coh(X)_{d-1}$</code> equivalent to <code>$\bigoplus_{x \in X_d} \mathcal{A}(\mathcal{O}_{X,x})$</code>?</p> <p>See: <a href="http://www.math.uni-bielefeld.de/~mseverit/algkalgc.pdf" rel="nofollow">http://www.math.uni-bielefeld.de/~mseverit/algkalgc.pdf</a> page 2, 6th equation.</p> <p>(cross post from <a href="http://math.stackexchange.com/questions/39186/quotient-category-coh-d-coh-d-1" rel="nofollow">http://math.stackexchange.com/questions/39186/quotient-category-coh-d-coh-d-1</a> )</p>