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On the coalgebraic ring and Bousfield-Kan spectral sequence for a Landweber exact spectrum

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journal contribution
posted on 2007-11-19, 15:46 authored by M. Bendersky, John R. Hunton
We construct a Bousfield–Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum E with unit and which is related to the homotopy groups of a certain unstable E completion X ∧ E of a space X. For E an S-algebra this completion agrees with that of the first author and Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) E∗ (E_∗ ) for an arbitrary Landweber exact spectrum E, extending work of the second author with Hopkins and with Turner and giving basis-free descriptions of the modules of primitives and indecomposables. Taken together, these results enable us to give a simple description of the E 2-page of the E-theory Bousfield–Kan spectral sequence when E is any Landweber exact ring spectrum with unit. This extends work of the first author and others and gives a tractable unstable Adams spectral sequence based on a νn-periodic theory for all n.

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Citation

Proceedings of the Edinburgh Mathematical Society, 2004, 47 (3), pp.513-532

Version

  • VoR (Version of Record)

Published in

Proceedings of the Edinburgh Mathematical Society

Publisher

Cambridge University Press (CUP)

issn

0013-0915

eissn

1464-3839

Copyright date

2004

Available date

2007-11-19

Publisher version

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2722132&fileId=S0013091503000518 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2722132

Language

en

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