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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

Let A1 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 EC be the second Morava E– theory associated to a universal deformation of the formal completion of the supersingular elliptic curve C : y2 + y = x3 defined over 𝔽4 and G24 a maximal finite subgroup of the automorphism group 𝕊C of the formal completion of C. We compute the homotopy groups of EChG24 A1 by means of the homotopy fixed-point spectral sequence.

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$K(2)$–local homotopy theory, topological modular forms, Davis–Mahowald spectral sequence, homotopy fixed-point spectral sequence
Mathematical Subject Classification
Primary: 55Q10
Received: 14 December 2020
Revised: 11 May 2021
Accepted: 8 June 2021
Published: 14 March 2023
Viet-Cuong Pham