Bewaard in:
| Hoofdauteur: | |
|---|---|
| Formaat: | Preprint |
| Gepubliceerd in: |
2017
|
| Onderwerpen: | |
| Online toegang: | https://arxiv.org/abs/1712.00521 |
| Tags: |
Voeg label toe
Geen labels, Wees de eerste die dit record labelt!
|
Inhoudsopgave:
- For any motivic $\mathbb{E}_\infty$-ring spectrum $A$ we construct an equivalence $ρ$ between the $\infty$-category of cellular motivic $A$-module spectra and modules over an $\mathbb{E}_1$-algebra $Θ$ in $\mathbb{Z} $-graded spectra, under which the motivic grading corresponds to the $\mathbb{Z}$-grading. If the base is the complex numbers or if $A$ admits an $\mathbb{E}_\infty$-orientation, we refine the $\mathbb{E}_1$-algebra $Θ$ to an $\mathbb{E}_\infty$-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 $\mathbb{E}_\infty$-algebra in $\mathcal{J} $-graded spectra that invert morphisms of $\mathcal{J}$, where $\mathcal{J}$ is the diagram category of Sagave-Schlichtkrull, a model for Quillen's localization of the groupoid of finite sets and bijections.