Note

The Picard group of E^{hG24}

Author: Wei Yang · Added: October 3, 2026

Abstract

Let $E$ be the height-two Morava $E$ -theory associated to the supersingular elliptic curve over $\mathbb{F}_4$ at the prime $2$ . We compute the Picard group of $K(2)$ -local $E^{hG_{24}}$ -modules. Suspension generates a cyclic group of order $192$ . The proof obtains an Artin-Schreier $d_{23}$ in the Picard descent spectral sequence from the $C_4$ calculation. Two finite Postnikov intervals determine the transfer needed for this differential. The Galois action on the remaining fifth filtration then excludes classes outside the suspension subgroup.