2017/12/01 by Heine, Hadrian
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1712.00521
For any motivic 𝔼_∞-ring spectrum A we construct an equivalence ρ between the ∞-category of cellular motivic A-module spectra and modules over an 𝔼1-algebra Θ in ℤ -graded spectra, under which the motivic grading corresponds to the ℤ-grading. If the base is the complex numbers or if A admits an 𝔼_∞-orientation, we refine the 𝔼1-algebra Θ to an 𝔼_∞-algebra and ρ to a symmetric monoidal equivalence. To capture the symmetric monoidal structure in the general situation, we lift ρ to a symmetric monoidal equivalence to modules over an 𝔼_∞-algebra in J -graded spectra that invert morphisms of J, where J is the diagram category of Sagave-Schlichtkrull, a model for Quillen's localization of the groupoid of finite sets and bijections.