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K-theory, reality, and duality

Published online by Cambridge University Press:  16 September 2014

Drew Heard  and
Vesna Stojanoska
Drew Heard
Affiliation:
Melbourne University, Australia, d.heard@student.unimelb.edu.au
Vesna Stojanoska
Affiliation:
Massachusetts Institute of Technology, Cambridge MA, USA, vstojanoska@math.mit.edu
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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 Σ4KU, 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.

Keywords

Anderson dualitydualizing complexK-theoryTate spectrumPicard group55N1519L9955M0555U3055P91
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 3 , December 2014 , pp. 526 - 555
Copyright
Copyright © ISOPP 2014 

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