On a universal characterisation of p-typical Witt vectors

For a prime p and a commutative ring R with unity, let $W(R)$ denote the ring of p-typical Witt vectors. The ring $W(R)$ is endowed with a Verschiebung operator W(R)VW(R) and a Teichm\"{u}ller map R \ W(R). One of the properties satisfied by V, \ is that the map R → W(R) given by x↦ V xᵖ - p x is an additive map. In this paper we show that for p≠ 2, this property essentially characterises the functor W. Unlike other characterisations, this only uses the group structure on $W(R)$ and hence is suitable for generalising to the non-commutative setup. We give a conjectural characterisation of Hesselholt's functor of p-typical Witt vectors using a universal property for p≠ 2. Moreover we provide evidence for this conjecture.