A criterion for regularity of local rings

Details A criterion for regularity of local rings A criterion for regularity of local rings

2006-02-11

arxiv.org/abs/math/0602235v2

Mathematics

Commutative Algebra

4 pages. Minor revisions. To appear in C. R. Acad. Sci. Paris, Ser. I

Scientific paper

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: M_i=0 for i not in [0,dim A]; the homology of M has finite length; H_0(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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