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Spectra of derived module homomorphisms

Published online by Cambridge University Press:  24 October 2008

Alan Robinson
Alan Robinson
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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Extract

We introduce a new construction in stable homotopy theory. If F and G are module spectra over a ring spectrum E, there is no well-known spectrum of E-module homomorphisms from F to G. Such a construction would not be homotopy invariant, and therefore would not serve much purpose. We show that, provided the rings and modules have A∞ structures, there is a spectrum RHomE(F, G) of derived module homomorphisms which has very pleasant properties. It is homotopy invariant, exact in each variable, and its homotopy groups form the abutment of a hypercohomology-type spectral sequence.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 249 - 257
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Klippenstein, J.. Applications of the universal coefficient theorem for connective K-theory. Ph.D. thesis, University of Warwick, 1985.Google Scholar
[2]Lewis, L. G., May, J. P., Mcclure, J. E. and Steinberger, M.. Equivariant Stable Homotopy Theory, Lecture Notes in Math. (to appear).Google Scholar
[3]Lin, T.-Y.. Adams type spectral sequences and stable homotopy modules. Indiana Univ. Math. J. 25 (1976), 135–158.CrossRefGoogle Scholar
[4]Robinson, C. A.. Derived tensor products in stable homotopy theory. Topology 22 (1983), 1–18.CrossRefGoogle Scholar
[5]Robinson, C. A.. Spectral sheaves: a model category for stable homotopy theory. J. Pure Appl. Algebra (in the Press).Google Scholar
[6]Stasheff, J. D.. Homotopy associativity of H-spaces I. Trans. Am. Math. Soc. 108 (1963), 275–292.Google Scholar