THE COTANGENT COMPLEX OF COMPLETE-INTERSECTIONS

Let X be an algebraic variety over a field k of characteristic 0 which is locally a complete intersection. In this Note, we show that the p-th graded exterior power of the cotangent complex L(X/k) is a resolution of the sheaf Omega(X/k)(p) Of differential p-forms provided that p less than or equal to r, where r is the codimension of the singular locus of X. This result admits an interpretation in terms of the Quillen decomposition of the Hochschild homology.