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Title: On the coalgebraic ring and Bousfield-Kan spectral sequence for a Landweber exact spectrum
Authors: Bendersky, M.
Hunton, John R.
First Published: 2004
Publisher: Cambridge University Press (CUP)
Citation: Proceedings of the Edinburgh Mathematical Society, 2004, 47 (3), pp.513-532
Abstract: 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.
DOI Link: 10.1017/S0013091503000518
ISSN: 0013-0915
eISSN: 1464-3839
Version: Publisher version
Status: Peer reviewed
Type: Article
Rights: Copyright © 2004 Cambridge University Press. Deposited with reference to the publisher's archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

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