2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108929It 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.4 pages. Minor revisions. To appear in C. R. Acad. Sci. Paris, Ser. ICommutative AlgebraAlgebraic Geometry13D22 (Primary) 13D 25; 14E99 (Secondary)text