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.
|Number of pages||15|
|Publication status||Published - 2020|