Invertible K(2)–local E–modules in C4–spectra

Beaudry, Agnès¹ ; Bobkova, Irina² ; Hill, Michael³ ; Stojanoska, Vesna⁴

¹Department of Mathematics, University of Colorado Boulder, Boulder, CO, United States
²Department of Mathematics, Texas A&M University, College Station, TX, United States
³Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, United States
⁴Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, IL, United States

Algebraic and Geometric Topology, Tome 20 (2020) no. 7, pp. 3423-3503

Résumé

We compute the Picard group of the category of K(2)–local module spectra over the ring spectrum EhC4, where E is a height 2 Morava E–theory and C4 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 C4–spectra. We show that in addition to a cyclic subgroup of order 32 generated by E ∧ S1, the Picard group contains a subgroup of order 2 generated by E ∧ S7+σ, where σ is the sign representation of the group C4. In the process, we completely compute the RO(C4)–graded Mackey functor homotopy fixed point spectral sequence for the C4–spectrum E“.

Détail

DOI : 10.2140/agt.2020.20.3423

Classification : 55P42, 55Q91, 20J06, 55M05, 55P60, 55Q51
Keywords: chromatic homotopy theory, Morava E–theory, Picard groups, higher real K–theory

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