Morphisms between two constructions of witt vectors of non-commutative rings

Abstract

Let A be any unital associative, possibly non-commutative ring and let p be a prime number. Let E(A) be the ring of p-typical Witt vectors as constructed by Cuntz and Deninger in [J. Algebra 440 (2015), pp. 545593] and let W(A) be the abelian group constructed by Hesselholt in [Acta Math. 178 (1997), pp. 109-141] and [Acta Math. 195 (2005), pp. 55-60]. In [J. Algebra 506 (2018), pp. 379-396] it was proved that if p = 2 and A is a non-commutative unital torsion free ring, then there is no surjective continu- ous group homomorphism from W(A) -> H H-0(E(A)) := E (A)/<([E (A), E(A)])over bar> which commutes with the Verschiebung operator and the Teichmiiller map. In this paper we generalise this result to all primes p and simplify the arguments used for p = 2. We also prove that if A a is a non-commutative unital ring, then there is no continuous map of sets H H-0(E(A)) -> W(A) which commutes with the ghost maps.