DubTop Seminar: Décalage

First introduced for chain complexes, Décalage “turns the page” of a spectral sequence and has since been generalized to cosimplicial objects and filtered spectra. We start with a cosimplicial spectrum \$X^\bullet\$ and filters its totalization via levelwise connective covers (equivalently, by totalizing the Whitehead tower), obtaining a filtered spectrum whose \$\mathrm{Tot}\$ spectral sequence is shifted forward: \$E_r(\mathrm{D\acute ec}^\Delta X^\bullet)\cong E_{r+1}(X^\bullet)\$. I will outline this construction, explain the page-shifting, and (if time permits) discuss applications to comparisons of spectral sequences including Adams–Novikov and slice filtrations.