Homology and K-Theory of Commutative Algebras: Characterization of Complete Intersections Original Research Article

In this paper, we study Hochschild homology, cyclic homology and K-theory of commutative algebras of finite type over a characteristic zero field. We prove that local complete intersections are characterized by HHin = 0 for i < n/ 2 or equivalently by HCin = 0 for i < n/ 2. For artinian algebras over a number field, we prove that local complete intersections are characterized by Kin = 0 for i < (n + 1)/ 2. This last result answers, in the particular case of artinian algebras over a number field, a famous conjecture of Beilinson and Soulé about the γ-filtration of the K-theory of a commutative algebra, module torsion.