Homotopy groups of $E_C^{h{G}_{24}}\wedge A_1$

Abstract

Let $A_1$ be any spectrum in a class of finite spectra whose mod $2$ cohomology is isomorphic to a free module of rank one over the subalgebra $\mathcal{A}(1)$ 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 group ${\mathbb{S}}_C$ of the formal completion of $C$. In this paper, we compute the homotopy groups of $E_C^{h{G}_{24}}\wedge A_1$ by means of the homotopy fixed point spectral sequence.

82 pages, 29 figures