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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.

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

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