The Chromatic E₁-term H⁰M₁² for p>3

Abstract:

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 $k$.

Department of Mathematics, Faculty of Science, Osaka City University
nakai@sci.osaka-cu.ac.jp
http://www.sci.osaka-cu.ac.jp/~nakai/