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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniqueness of $E_\infty$ structures for connective covers
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by Andrew Baker and Birgit Richter PDF
Proc. Amer. Math. Soc. 136 (2008), 707-714 Request permission

Abstract:

We refine our earlier work on the existence and uniqueness of $E_\infty$ structures on $K$-theoretic spectra to show that the connective versions of real and complex $K$-theory as well as the connective Adams summand $\ell$ at each prime $p$ have unique structures as commutative $\mathbb {S}$-algebras. For the $p$-completion $\ell _p$ we show that the McClure-Staffeldt model for $\ell _p$ is equivalent as an $E_\infty$ ring spectrum to the connective cover of the periodic Adams summand $L_p$. We establish a Bousfield equivalence between the connective cover of the Lubin-Tate spectrum $E_n$ and $BP\langle n\rangle$.
References
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Additional Information
  • Andrew Baker
  • Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
  • MR Author ID: 29540
  • ORCID: 0000-0002-9369-7702
  • Email: a.baker@maths.gla.ac.uk
  • Birgit Richter
  • Affiliation: Department Mathematik der Universität Hamburg, 20146 Hamburg, Germany
  • Email: richter@math.uni-hamburg.de
  • Received by editor(s): October 10, 2006
  • Received by editor(s) in revised form: October 25, 2006
  • Published electronically: November 2, 2007
  • Additional Notes: The first author thanks the Max-Planck Institute and the mathematics department in Bonn.
    The second author was partially supported by the Strategisk Universitetsprogram i Ren Matematikk (SUPREMA) of the Norwegian Research Council.
  • Communicated by: Paul Goerss
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 707-714
  • MSC (2000): Primary 55P43, 55N15; Secondary 19L41
  • DOI: https://doi.org/10.1090/S0002-9939-07-08984-8
  • MathSciNet review: 2358512