On the vanishing of Hochschild homology of locally complete intersections (Q911679)

Let K be a field of characteristic zero, let A be a locally complete intersection K-algebra, and let \(H_ n(A,A)\) denote the Hochschild homology of A. We prove that there exists a convergent spectral sequence \[ E^ 2_{p,q}=H_ p(A,A)\otimes_ A\bigwedge^ qJ/J^ 2 \Rightarrow A\otimes_ R\Omega^ n_{R| K}, \] where R is a polynomial K-algebra of finite type such that \(A=R/J\). We use it to obtain the following result: If \(H_ n(A,A)=0\) for n sufficiently large, then A is a smooth K-algebra.