The universal deformation of the Witt ring scheme

We determine the universal deformation over reduced base rings of the Witt ring scheme enhanced by a Frobenius lift and Verschiebung. It agrees with a $q$-deformation introduced earlier by the second author; we also give a simpler description for this. In the appendix we discuss a Witt vector theory for ind-rings which may be of independent interest.
Bibliography: 7 titles.