The units of a ring spectrum and a logarithmic cohomology operation

Rezk, Charles

doi:10.1090/S0894-0347-06-00521-2

The units of a ring spectrum and a logarithmic cohomology operation
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by Charles Rezk

J. Amer. Math. Soc. 19 (2006), 969-1014

DOI: https://doi.org/10.1090/S0894-0347-06-00521-2

Published electronically: February 8, 2006

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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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