A criterion for regularity of local rings
Tom Bridgeland, Srikanth Iyengar
Abstract
It is proved that a noetherian commutative local ring A containing a field is regular if there is a complex M of free A-modules with the following properties: Mi=0 for i not in [0,dim A]; the homology of M has finite length; H0(M) contains the residue field of A as a direct summand. This result is an essential component in the proofs of the McKay correspondence in dimension 3 and of the statement that threefold flops induce equivalences of derived categories.
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