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

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.