Higher semiadditive algebraic K-theory and redshift

Shay Ben-Moshe, Tomer M. Schlank

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We define higher semiadditive algebraic K-theory, a variant of algebraic K-theory that takes into account higher semiadditive structure, as enjoyed for example by the - and -local categories. We prove that it satisfies a form of the redshift conjecture. Namely, that if is a ring spectrum of height, then its semiadditive K-theory is of height. Under further hypothesis on, which are satisfied for example by the Lubin-Tate spectrum, we show that its semiadditive algebraic K-theory is of height exactly. Finally, we connect semiadditive K-theory to -localized K-theory, showing that they coincide for any -invertible ring spectrum and for the completed Johnson-Wilson spectrum.

Original languageAmerican English
Pages (from-to)237-287
Number of pages51
JournalCompositio Mathematica
Volume160
Issue number2
DOIs
StatePublished - 15 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s).

Keywords

  • algebraic K-theory
  • ambidexterity
  • chromatic homotopy theory
  • higher semiadditivity
  • redshift

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