TL;DR
This paper extends the theory of Witt vectors into the almost mathematics setting and applies these results to almost purity, providing a new proof for rank one valuation rings.
Contribution
It introduces Witt vectors in the almost category and applies these results to almost purity, offering a novel proof for rank one valuation rings.
Findings
Witt vectors are developed in the almost category.
A new proof for almost purity in rank one valuation rings.
Enhanced understanding of almost mathematics in valuation theory.
Abstract
Our main goal in this paper is to prove results for Witt vectors in the almost category. We finish with an application to almost purity, in particular offering a new proof for rank one valuation rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Advanced Banach Space Theory