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$\mathbf{A}_{\text {inf}}$ has uncountable Krull dimension (2002.10358v3)
Published 24 Feb 2020 in math.NT and math.AC
Abstract: Let $\mathcal{O}E$ be a complete discrete valuation ring and $R$ be a perfect ring in characteristic $p$, we also assume $R$ is a complete valuation ring whose valuation group is of rank one and non-discrete, we prove the Krull dimension of the ring $W{\mathcal{O}_E}(R)$ of $\mathcal{O}_E$-Witt vectors over $R$ is at least the cardinality of the continuum.
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