Remarks on K(1)-local K-theory

2020/01/31 by Bhatt, Bhargav, Clausen, Dustin, Mathew, Akhil · 1 citation
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2001.11622

Abstract

We prove two basic structural properties of the algebraic K-theory of rings after K(1)-localization at an implicit prime p. Our first result (also recently obtained by Land--Meier--Tamme by different methods) states that L_K(1) K(R) is insensitive to inverting p on R; we deduce this from recent advances in prismatic cohomology and TC. Our second result yields a Künneth formula in K(1)-local K-theory for adding p-power roots of unity to R.

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• K(1)-local K-theory of Azumaya algebras

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