Greenberg algebras and ramified Witt vectors
Alessandra Bertapelle, Maurizio Candilera

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Advanced Topics in Algebra
