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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {O}_E\)</EquationSource> </InlineEquation> be a complete discrete valuation ring and <Emphasis Type="BoldItalic">R</Emphasis> be a perfect ring in characteristic <Emphasis Type="BoldItalic">p</Emphasis>, we also assume <Emphasis Type="BoldItalic">R</Emphasis> is a valuation ring whose valuation group is of rank one and non-discrete, we prove the Krull dimension of the ring <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(W_{\mathcal {O}_E}(R)\)</EquationSource> </InlineEquation> of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {O}_E\)</EquationSource> </InlineEquation>-Witt vectors over <Emphasis Type="BoldItalic">R</Emphasis> is at least the cardinality of the continuum.</p>

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Ainf has uncountable Krull dimension

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Du Heng

摘要

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 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.