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Spectra of derived module homomorphisms. (English) Zbl 0635.55011
The author has worked extensively in stable homotopy, especially the theory of spectra [see, e.g., Topology 22, 1-18 (1983; Zbl 0519.55004)]. The purpose of the present note is to introduce a homomorphism spectrum between module spectra over a given ring spectrum. This is carried out in the case where the ring and module spectra have \(A_{\infty}\) structures. The resulting homomorphism spectrum has many pleasant properties, e.g., it is a homotopy invariant, exact in each variable, and reduces to the more traditional mapping spectrum when the ring spectrum is that of spheres. The author also constructs a spectral sequence.
These results specialize to known work in several cases, including work of J. Klippenstein on Brown-Gitler spectra [Thesis, Univ. Warwick (1985)] and the Adams-like spectral sequence of Brayton Gray (unpublished) and T. Y. Lin [Indiana Univ. Math. J. 25, 135-158 (1976; Zbl 0333.55013)].
Reviewer: D.W.Kahn

MSC:
55P42 Stable homotopy theory, spectra
55P65 Homotopy functors in algebraic topology
55T25 Generalized cohomology and spectral sequences in algebraic topology
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[1] DOI: 10.2307/1993608 · Zbl 0114.39402
[2] DOI: 10.1512/iumj.1976.25.25011 · Zbl 0333.55013
[3] DOI: 10.1016/0040-9383(83)90042-3 · Zbl 0519.55004
[4] Robinson, J. Pure Appl. Algebra
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