On homotopy groups of EChG24∧A1

Abstract

Let $A(1)$ be any of the four finite spectra whose cohomology is isomorphic to the subalgebra $A(1)$ of the Steenrod algebra. Let $E_{C}$ be the second Morava-$E$ theory associated to a universal deformation of the formal completion of the supersingular elliptic curve $(C) : y^{2}+y = x^{3}$ defined over $\mathbb{F}_{4}$ and $G_{24}$ a maximal finite subgroup of automorphism groups $\mathbb{S}_{C}$ of the formal completion $F_{C}$. In this paper, we will compute the homotopy groups of $E_{C}^{hG_{24}}\wedge A(1)$ by means of the homotopy fixed point spectral sequence.