On the chromatic Ext 0 ( M 1 n − 1 ) on Γ ( m + 1 ) for an odd prime

Let M1 n−1 denote the cokernel of the localization map BP∗/I → v−1 n−1BP∗/I, where I denotes the ideal of BP∗ generated by vi’s for 0 ≤ i ≤ n − 2. The chromatic Ext0(M1 n−1) on Γ(m + 1), which we denote Ex0(m, n), is isomorphic to the 0-th line of the E2-term of the Adams-Novikov spectral sequence for computing the homotopy groups of a spectrum, whose BP∗-homology is M1 n−1 ⊗BP∗ BP∗[t1, t2, . . . , tm] for the generators ti of BP∗BP . In [9], the homotopy groups of such a spectrum are determined for m + 1 ≥ n(n − 1) by computing Ex∗(m, n). The 0-th line Ex0(m, 3) is determined by Ichigi, Nakai and Ravenel [1]. Here, we determine the 0-th line Ex0(m, n) under the condition: (n− 1)2 ≤ m + 1 < n(n− 1) and n ≥ 4.