A_inf is infinite dimensional

2019/06/09 by Jaclyn Lang, Lang, Jaclyn, Judith Ludwig +1
Mathematics · #13F25 #13F35 #14F30 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1906.03583

openalex publication_date 2019/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a perfect valuation ring R of characteristic p that is complete with respect to a rank-1 nondiscrete valuation, we show that the ring A_inf of Witt vectors of R has infinite Krull dimension.

Related

• A_\text inf has uncountable Krull dimension
• Some ring-theoretic properties of A_inf
• Almost Witt Vectors
• Completions of valuation rings
• Arithmetical Rings and Krull Dimension