Witt vector rings and quotients of monoid algebras

TL;DR

This paper provides explicit descriptions of the isomorphisms between certain quotients of monoid algebras and Witt rings for perfect a5_p-algebras, extending previous work on the ring C(R).

Contribution

It explicitly describes the isomorphisms _n for n  p, advancing understanding of Witt vector rings and their relation to monoid algebra quotients.

Findings

Explicit descriptions of _n for n  p.

Clarification of the structure of Witt rings for perfect a5_p-algebras.

Extension of previous isomorphism results to higher n.

Abstract

In a previous paper Cuntz and Deninger introduced the ring $C(R)$ for a perfect $\mathbb{F}_p$-algebra $R$. The ring $C(R)$ is canonically isomorphic to the $p$-typical Witt ring $W(R)$. In fact there exist canonical isomorphisms $\alpha_n \colon \mathbb{Z}R/I^n \xrightarrow{\sim} W_n(R)$. In this paper we give explicit descriptions of the isomorphisms $\alpha_n$ for $n\geq 2$ if $p\geq n$.