Remarks on K(1)-local K-theory

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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 LK(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.
Original languageEnglish
Article number39
JournalSelecta Mathematica
Issue number3
Number of pages15
Publication statusPublished - 2020
Externally publishedYes

ID: 259823810