The derived category of complex periodic K-theory localized at an odd prime

Irakli Patchkoria*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We prove that for an odd prime p, the derived category D(KU_(p))
of the p-local complex periodic K-theory spectrum KU_(p) is triangulated equivalent to the derived category of its homotopy ring pi_*KU_(p). This implies that if p is an odd prime, the triangulated category D(KU_(p)) is algebraic.
Original languageEnglish
Pages (from-to)392-435
Number of pages43
JournalAdvances in Mathematics
Early online date16 Feb 2017
Publication statusPublished - 17 Mar 2017

Bibliographical note

First of all I would like to thank Tyler Lawson and Stefan Schwede for their interest in the subject and for encouraging me to think about this problem. Special thanks go to Dustin Clausen for answering my questions in Galois theory and to Moritz Groth for tutorials on derivators. I would also like to thank Rasmus Bentmann, Jens Franke, John Greenlees, Snigdhayan Mahanta, George Nadareishvili and Constanze Roitzheim for useful conversations. Finally, I thank the referee for helpful comments.
This research was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the Shota Rustaveli National Science Foundation grant DI/27/5-103/12.


  • Derivator
  • Model category
  • K-theory
  • Module spectrum
  • Stable model category
  • Triangulated category


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