A descent view on Mitchell's theorem

2020/08/06 by Elden Elmanto, Elmanto, Elden, Denis Nardin +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2008.02821

openalex publication_date 2020/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we given a new proof of Mitchell's theorem that L_T(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.

Citations

• Algebraic K-theory of topological K-theory
• On motivic cohomology with Z/l coefficients

Cited by

• The Redshift Bound from Quillen-Lichtenbaum

Related

• Examples of chromatic redshift in algebraic K-theory
• Beilinson-Bernstein localization over the Harish-Chandra center
• A short proof of w₁ⁿ(Hom(C_2r+1, K_n+2))=0 for all n and a graph colouring theorem by Babson and Kozlov
• Descent and vanishing in chromatic algebraic K-theory via group actions
• Topological Colored Tverberg Theorem and the Reduction Lemma