On the 2-typical de Rham-Witt complex

Abstract

In this paper we introduce the 2-typical de Rham-Witt complex for arbitrary commutative, unital rings and log-rings. We describe this complex for the rings $\mathbb{Z}$ and ${\mathbb{Z}}_{(2)}$, for the log-ring $({\mathbb{Z}}_{(2)},M)$ with the canonical log-structure, and we describe its behaviour under polynomial extensions. In an appendix we also describe the $p$-typical de Rham-Witt complex of $({\mathbb{Z}}_{(p)},M)$ for $p$ odd.