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Remarks on K(1)-local K-theory

    1. [1] University of Michigan–Ann Arbor

      University of Michigan–Ann Arbor

      City of Ann Arbor, Estados Unidos

    2. [2] Max Planck Institute for Mathematics

      Max Planck Institute for Mathematics

      Kreisfreie Stadt Bonn, Alemania

    3. [3] University of Chicago

      University of Chicago

      City of Chicago, Estados Unidos

  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
  • Idioma: inglés
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  • Resumen
    • 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.


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