Greenberg algebras and ramified Witt vectors

TL;DR

This paper investigates the relationship between Greenberg algebras and ramified Witt vectors over a complete discrete valuation ring, revealing a universal homeomorphism with explicit kernel descriptions in certain cases.

Contribution

It introduces a natural morphism connecting Greenberg algebras and ramified Witt vectors, providing explicit descriptions of its kernel and topological properties.

Findings

The morphism is a universal homeomorphism.

The kernel of the morphism is pro-infinitesimal and explicitly describable.

The study enhances understanding of the structure of ramified Witt vectors.

Abstract

Let O be a complete discrete valuation ring of mixed characteristic and with finite residue field k. We study a natural morphism between the Greenberg algebra of O and the special fiber of the scheme of ramified Witt vectors over O. It is a universal homeomorphism with pro-infinitesimal kernel that can be explicitly described in some cases.