The Universal Deformation of the Witt Ring Scheme

TL;DR

This paper characterizes the universal deformation of the Witt ring scheme with Frobenius and Verschiebung, linking it to a known q-deformation and providing a simplified description and a Witt vector theory for ind-rings.

Contribution

It identifies the universal deformation of the Witt ring scheme with Frobenius and Verschiebung, connecting it to a q-deformation and introducing a Witt vector theory for ind-rings.

Findings

Universal deformation matches a known q-deformation.

Simplified description of the q-deformation.

Witt vector theory for ind-rings discussed.

Abstract

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 earlier introduced by the second author, for which we also give a simpler description. In the appendix we discuss a Witt vector theory for ind-rings which may be of independent interest.