K-theory, reality, and duality

Drew Heard, Vesna Stojanoska

Research output: Contribution to journalArticle

Abstract

We present a new proof of Anderson's result that the real K-theory spectrum is Anderson self-dual up to a fourfold suspension shift; more strongly, we show that the Anderson dual of the complex K-theory spectrum KU is C2- equivariantly equivalent to Σ4 KU, where C2 acts by complex conjugation. We give an algebro-geometric interpretation of this result in spectrally derived algebraic geometry and apply the result to calculate 2-primary Gross-Hopkins duality at height 1. From the latter we obtain a new computation of the group of exotic elements of the K(1)-local Picard group.

Original languageEnglish (US)
Pages (from-to)526-555
Number of pages30
JournalJournal of K-Theory
Volume14
Issue number3
DOIs
StatePublished - Jul 8 2014
Externally publishedYes

Keywords

  • Anderson duality
  • K-theory
  • Picard group
  • Tate spectrum
  • dualizing complex

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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