On the 2-typical de Rham-Witt complex

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.

💡 Research Summary

The paper introduces a fully fledged 2‑typical de Rham‑Witt complex that works for any commutative unital ring and for log‑rings. The authors begin by recalling the classical p‑typical de Rham‑Witt construction and point out that the case p = 2 requires special treatment because the usual identities involving the Frobenius (F), Verschiebung (V) and the differential d acquire extra 2‑torsion phenomena. To address this, they define a new complex (W_{(2)}\Omega_R^\ast) whose underlying graded module in degree 0 is the ring of 2‑typical Witt vectors (W_{(2)}(R)) and whose higher degrees are built from formal symbols (d