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On the homotopy groups of E(n)–local spectra with unusual invariant ideals

Hirofumi Nakai and Katsumi Shimomura

Geometry & Topology Monographs 10 (2007) 319–332

DOI: 10.2140/gtm.2007.10.319

arXiv: 0903.4662


Let E(n) and T(m) for nonnegative integers n and m denote the Johnson--Wilson and the Ravenel spectra, respectively. Given a spectrum whose E(n)*–homology is E(n)*(T(m))/(v1,…,vn-1), then each homotopy group of it estimates the order of each homotopy group of LnT(m). We here study the E(n)–based Adams E2–term of it and present that the determination of the E2–term is unexpectedly complex for odd prime case. At the prime two, we determine the E–term for π*(L2T(1)/(v1)), whose computation is easier than that of π*(L2T(1)) as we expect.


Ravenel spectrum, Bousfield localization, Johnson–Wilson spectrum, Adams–Novikov spectral sequence

Mathematical Subject Classification

Primary: 55Q99


Received: 31 August 2004
Revised: 16 September 2005
Published: 18 April 2007

Hirofumi Nakai
Department of Mathematics
Faculty of Technology
Musashi Institute of Technology
Tokyo 158-8557
Katsumi Shimomura
Department of Mathematics
Faculty of Science
Kochi University
Kochi 780-8520