A universal group-theoretic characterisation of p-typical Witt vectors

Abstract

For a prime p and a commutative ring R with unity, let denote the group of p-typical Witt vectors. The group is endowed with a Verschiebung operator and a Teichmüller map . One of the properties satisfied by is that the map given by is an additive map. In this paper we show that for , this property essentially characterises the functor W (Theorem 1.6). Unlike other characterisations (see [1], [7]), this is a group-theoretic characterisation, in the sense that it does not use the ring structure of . Most constructions of the group of p-typical Witt vectors of non-commutative rings do not have a ring structure, and hence the above characterisation is more suitable for generalisation to the non-commutative setup.