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<p>In this short note, we give a new proof of Mitchell’s theorem that L<sub>T(<i>n</i>)</sub>K(<b>Z</b>) ≃ 0 for <i>n</i> ⩾ 2. Instead of reducing the problem to delicate representation theory, we use recently established hyperdescent technology for chromatically-localized algebraic K-theory.</p>

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A Descent view on Mitchell’s theorem

  • 期刊论文

  • 发表日期：

    2025年5月9日

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  • Elden Elmanto,
  • Denis Nardin,
  • Lucy Yang

摘要

In this short note, we give a new proof of Mitchell’s theorem that LT(n)K(Z) ≃ 0 for n ⩾ 2. Instead of reducing the problem to delicate representation theory, we use recently established hyperdescent technology for chromatically-localized algebraic K-theory.