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

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

2009-03-26

arxiv.org/abs/0903.4662v1

Geom. Topol. Monogr. 10 (2007) 319-332

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 18 April 2007

Scientific paper

10.2140/gtm.2007.10.319

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))/(v_1,...,v_{n-1}), then each homotopy group of it estimates the order of each homotopy group of L_nT(m). We here study the E(n)-based Adams E_2-term of it and present that the determination of the E_2-term is unexpectedly complex for odd prime case. At the prime two, we determine the E_{infty}-term for pi_*(L_2T(1)/(v_1)), whose computation is easier than that of pi_*(L_2T(1)) as we expect.

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