On homotopy groups of EChG24 ∧A1

Pham, Viet-Cuong

doi:10.2140/agt.2022.22.3855

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On homotopy groups of $E_C^{hG_{24}}\wedge A_1$

Viet-Cuong Pham

Algebraic & Geometric Topology 22 (2022) 3855–3938

DOI: 10.2140/agt.2022.22.3855

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 $𝒜 (1)$ 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 $𝔽_{4}$ and $G_{24}$ a maximal finite subgroup of the automorphism group $𝕊_{C}$ of the formal completion of $C$ . We compute the homotopy groups of $E_{C}^{h G_{24}} \land A_{1}$ by means of the homotopy fixed-point spectral sequence.

Keywords

$K(2)$–local homotopy theory, topological modular forms, Davis–Mahowald spectral sequence, homotopy fixed-point spectral sequence

Mathematical Subject Classification

Primary: 55Q10

References

Publication

Received: 14 December 2020

Revised: 11 May 2021

Accepted: 8 June 2021

Published: 14 March 2023

Authors

Viet-Cuong Pham
MPIM Bonn Bonn Germany

Volume 22, issue 8 (2022)