On the rigidity of the generalized Koszul complexes with applications to Hochschild homology (Q1330035)

This paper is a new step in the saga of papers concerning the vanishing of the Hochschild homology and the smoothness of an algebra. In Comment. Math. Helv. 69, 163-168 (1994), the group BACH (Buenos Aires Cyclic Homology Group) proved a result conjectured by the author: Let \(\kappa\) be a field of characteristic zero and let \(A\) be a commutative \(\kappa\)-algebra of finite type. The vanishing of the Hochschild homology \(H_ * (A,A)\) in an odd and an even degree suffices for \(A\) to be smooth. -- In the present paper the author conjectures that for a field \(\kappa\) of arbitrary characteristic and a \(\kappa\)-algebra \(A\) essentially of finite type, if \(H_ p (A,A) = 0\) for some natural number \(p\), then \(A\) is smooth. Using the relationship between \(H_ * (A,A)\) and the homology of the generalized Koszul complexes, he proves his conjecture for locally complete intersections.