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\"uller map R \ (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.