Pseudovaluations on the De Rham-Witt complex

TL;DR

This paper introduces pseudovaluations on the de Rham-Witt complex for polynomial rings over rings of positive characteristic, enabling explicit computations and reconstruction of the overconvergent complex.

Contribution

It defines pseudovaluations on the de Rham-Witt complex and demonstrates their use in explicit product computations and recovering the overconvergent complex.

Findings

Pseudovaluations are established on the de Rham-Witt complex.

Explicit product formulas for basic elements are derived.

Overconvergent de Rham-Witt complex can be reconstructed using these pseudovaluations.

Abstract

For a polynomial ring over a commutative ring of positive characteristic, we define on the associated de Rham-Witt complex a set of functions, and show that they are pseudovaluations in the sense of Davis, Langer and Zink. To achieve it, we explicitly compute products of basic elements on the complex. We also prove that the overconvergent de Rham-Witt complex can be recovered using these pseudovaluations.