A_inf IS INFINITE DIMENSIONAL

<jats:p>Given a perfect valuation ring <jats:inline-formula>
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<jats:tex-math>$R$</jats:tex-math>
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</jats:inline-formula> of characteristic <jats:inline-formula>
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<jats:tex-math>$p$</jats:tex-math>
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</jats:inline-formula> that is complete with respect to a rank-<jats:inline-formula>
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<jats:tex-math>$1$</jats:tex-math>
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</jats:inline-formula> nondiscrete valuation, we show that the ring <jats:inline-formula>
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<jats:tex-math>$\mathbb{A}_{\inf }$</jats:tex-math>
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</jats:inline-formula> of Witt vectors of <jats:inline-formula>
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<jats:tex-math>$R$</jats:tex-math>
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</jats:inline-formula> has infinite Krull dimension.</jats:p>