Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T07:48:33.381Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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