most recent 30 from http://mathoverflow.net 2013-05-19T00:10:43Z http://mathoverflow.net/feeds/user/3833 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/14350/existence-of-non-commutative-desingularizations/14360#14360 Brian Jurgelewicz 2010-02-06T05:14:24Z 2010-02-06T05:14:24Z

<p>If you haven't already, definitely check out the paper by Burban Iyama Keller and Reiten on Cluster Tilting for One-Dimensional Hypersurface Singularities.</p> <p>Also, you may google "Auslander representation dimension." It is defined by rep.dim(R) = inf{gl.dim(End_R(M)) | M is a generator-cogenerator}. </p> <p>In the ADE case the preprojective algebra of the affine dynkin quiver arises this way, and it has finite global dimension.</p> <p>But you are dropping the condition that M be a generator-cogenerator.</p> <p>Here is a very general result of Van den Bergh: Assume X is separated. Then there exists a perfect complex E such that D(Qcoh X) is equivalent to D(A) where A is the DG-algebra RHom_X(E,E).</p> <p>Here is another article which is highly related: D. Orlov, Remarks on generators and dimensions of triangulated categories.</p>