2025/03/06 by Phil Pützstück, Pützstück, Phil · 1 citation
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2503.04456
We answer a question of Schwede on the existence of global Picard spectra associated to his ultra-commutative global ring spectra; given an ultra-commutative global ring spectrum R, we show there exists a global spectrum piceq(R) assembling the Picard spectra of all underlying G-equivariant ring spectra resG R of R into one object, in that for all finite groups G, the genuine fixed points are given by piceq(R)G ≃ pic(ModresG R(SpG)). Along the way, we develop a generalization of Borel-equivariant objects in the setting of parametrized higher algebra. We use this to assemble the symmetric monoidal categories of G-spectra for all finite groups G together with all restrictions and norms into a single `normed global category', and build a comparison functor which allows us to import ultra-commutative G-equivariant or global ring spectra into the setting of parametrized higher algebra.