Invertible K(2)-local E-modules in C-4-spectra Academic Article uri icon

abstract

  • We compute the Picard group of the category of $K(2)$-local module spectra over the ring spectrum $E^{hC_4}$, where $E$ is a height 2 Morava $E$-theory and $C_4$ is a subgroup of the associated Morava stabilizer group. This group can be identified with the Picard group of $K(2)$-local $E$-modules in genuine $C_4$-spectra. We show that in addition to a cyclic subgroup of order 32 generated by $ Ewedge S^1$ the Picard group contains a subgroup of order 2 generated by $Ewedge S^{7+sigma}$, where $sigma$ is the sign representation of the group $C_4$. In the process, we completely compute the $RO(C_4)$-graded Mackey functor homotopy fixed point spectral sequence for the $C_4$-spectrum $E$.

published proceedings

  • ALGEBRAIC AND GEOMETRIC TOPOLOGY

altmetric score

  • 0.5

author list (cited authors)

  • Beaudry, A., Bobkova, I., Hill, M., & Stojanoska, V.

citation count

  • 5

complete list of authors

  • Beaudry, Agnes||Bobkova, Irina||Hill, Michael||Stojanoska, Vesna

publication date

  • December 2020