Hochschild-Witt complex.

In a previous paper, we have defined polynomial Witt vectors functor from vector spaces over a perfect field k of positive characteristic p to abelian groups. In this paper, we use polynomial Witt vectors to construct a functorial Hochschild-Witt complex W C H ⁎ (A) for any associative unital k -algebra A , with homology groups W H H ⁎ (A). We prove that the group W H H 0 (A) coincides with the group of non-commutative Witt vectors defined by Hesselholt, while if A is commutative, finitely generated, and smooth, the groups W H H i (A) are naturally identified with the terms W Ω A i of the de Rham-Witt complex of the spectrum of A. [ABSTRACT FROM AUTHOR]