2019/01/31 by Agnès Beaudry, Agnes Beaudry, Irina Bobkova +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Fixed point #Functor #Group (periodic table) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Invertible matrix #Order (exchange) #Picard group #Spectrum (functional analysis) #math.AT #msc:20J06 #msc:55M05 #msc:55P42 #msc:55P60 #msc:55Q51 #msc:55Q91
paper · pdf · doi:10.2140/agt.2020.20.3423
published as Algebr. Geom. Topol. 20 (2020) 3423-3503
openalex created_date 2019/01/25 · openalex publication_date 2020/12/29 · arxiv created 2021/01/28 · arxiv updated 2021/01/29 · openalex updated_date 2026/08/05
We compute the Picard group of the category of [math] –local module spectra over the ring spectrum [math] , where [math] is a height [math] Morava [math] –theory and [math] is a subgroup of the associated Morava stabilizer group. This group can be identified with the Picard group of [math] –local [math] –modules in genuine [math] –spectra. We show that in addition to a cyclic subgroup of order [math] generated by [math] , the Picard group contains a subgroup of order [math] generated by [math] , where [math] is the sign representation of the group [math] . In the process, we completely compute the [math] –graded Mackey functor homotopy fixed point spectral sequence for the [math] –spectrum [math] .