The units of a ring spectrum and a logarithmic cohomology operation

Rezk, Charles¹

¹ Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61820

Journal of the American Mathematical Society, Tome 19 (2006) no. 4, pp. 969-1014

Résumé

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.

Détail

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

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