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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The units of a ring spectrum and a logarithmic cohomology operation
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by Charles Rezk PDF
J. Amer. Math. Soc. 19 (2006), 969-1014 Request permission

Abstract:

We construct a “logarithmic” cohomology operation on Morava $E$-theory, which is a homomorphism defined on the multiplicative group of invertible elements in the ring $E^0(K)$ of a space $K$. We obtain a formula for this map in terms of the action of Hecke operators on Morava $E$-theory. Our formula is closely related to that for an Euler factor of the Hecke $L$-function of an automorphic form.
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Additional Information
  • Charles Rezk
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61820
  • MR Author ID: 638495
  • ORCID: 0000-0003-4111-893X
  • Email: rezk@math.uiuc.edu
  • Received by editor(s): April 5, 2005
  • Published electronically: February 8, 2006
  • Additional Notes: This work was supported by the National Science Foundation under award DMS-0203936.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 969-1014
  • MSC (2000): Primary 55N22; Secondary 55P43, 55S05, 55S25, 55P47, 55P60, 55N34, 11F25
  • DOI: https://doi.org/10.1090/S0894-0347-06-00521-2
  • MathSciNet review: 2219307