Descent and vanishing in chromatic algebraic K-theory via group actions

2020/11/16 by Dustin Clausen, Akhil Mathew, Clausen, Dustin +5 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2011.08233

openalex publication_date 2020/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove some K-theoretic descent results for finite group actions on stable ∞-categories, including the p-group case of the Galois descent conjecture of Ausoni-Rognes. We also prove vanishing results in accordance with Ausoni-Rognes's redshift philosophy: in particular, we show that if R is an 𝔼_∞-ring spectrum with L_T(n)R=0, then L_T(n+1)K(R)=0. Our key observation is that descent and vanishing are logically interrelated, permitting to establish them simultaneously by induction on the height.

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