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The units of a ring spectrum and a logarithmic cohomology operation


Author: Charles Rezk
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
Published electronically: February 8, 2006
MathSciNet review: 2219307
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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
Email: rezk@math.uiuc.edu

DOI: https://doi.org/10.1090/S0894-0347-06-00521-2
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.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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