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New York Journal of Mathematics 6 (2000), 21-54.

The Chromatic E1-term H0M12 for p>3

Hirofumi Nakai

Published: February 1, 2000
Keywords: Stable homotopy of spheres, Adams-Novikov spectral sequence, chromatic spectral sequence
Subject: 55Q45; secondary 55Q51, 55T15, 55N22


In this paper, study the module structure of \[{\rm Ext}_{BP_*BP}^0(BP_*, BP_*/(p , v_1^\infty , v_2^\infty )),\] which is regarded as the chromatic $E_1$-term converging to the second line of the Adams-Novikov $E_2$-term for the Moore spectrum. The main difficulty here is to construct elements $x(sp^r/j;k)$ from the Miller-Ravenel-Wilson elements $(x_{3,r}^s/v_2^j)^{p^k} \in H^0M_2^1$. We achieve this by developing some inductive methods of constructing $x(sp^r/j;k)$ on $k$.

Author information:
Department of Mathematics, Faculty of Science, Osaka City University