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am starting something at logarithmic cohomology operation, but so far there are just some general statements and some references
One more reference: the “logarithmic operation” for p-complete K-theory was first described by tom Dieck (though not in relation to the Bousfield-Kuhn functor).
tom Dieck, Tammo(D-GTN) The Artin-Hasse logarithm for λ-rings. Algebraic topology (Arcata, CA, 1986), 409–415, Lecture Notes in Math., 1370, Springer, Berlin, 1989.
Thanks! I have put that in now (see here).
So you are the first to formulate the log operations via Bousfield-Kuhn, right? That’s how the entry currently attributes it, anyway. Please check, if you have another second.
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