On the 2-typical de Rham-Witt complex

TL;DR

This paper introduces the 2-typical de Rham-Witt complex for general rings and log-rings, detailing its structure for specific rings and its behavior under polynomial extensions, with additional results for odd primes.

Contribution

It provides a new construction of the 2-typical de Rham-Witt complex applicable to arbitrary rings and log-rings, expanding understanding of its structure and properties.

Findings

Describes the 2-typical de Rham-Witt complex for nd nd log-rings

Analyzes the behavior under polynomial extensions

Includes description of the p-typical complex for odd primes

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 \Z and \Z_{(2)}, for the log-ring (\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 (\Z_{(p)},M) for p odd.