On the comparison of two constructions of Witt vectors of non-commutative rings

Abstract

Let $A$ be any associative ring , possibly non-commutative, and let $p$ be a prime number. Let $E(A)$ be the ring of $p$-typical Witt vectors as constructed by Cuntz and Deninger and $W(A)$ be that constructed by Hesselholt. The goal of this paper is to answer the following question by Hesselholt: Is $HH_0(E(A)) $ isomorphic to $W(A)$? We show that in the case $p=2$, there is no such isomorphism possible if one insists it to be compatible with the Verscheibung operator and the Teichm\"uller map.