Konstantin Emming (Wayne State University)

  Empirical evidence suggests that there is an interesting class of motivic spectra (containing for example the sphere spectrum and Hermitian K-theory) whose effective motivic slices are indexed by the Adams-Novikov E_2-page of their Betti realizations. In this talk, we will show that there are more C-motivic spectra satisfying this property. For example, the C-motivic modular forms spectrum mmf. Our approach to this problem will also recompute the slices of the aforementioned spectra.

 The results rely on the filtered spectrum model for C-motivic (stable, cellular, 2-complete) homotopy theory due to Gheorghe-Isaksen-Krause-Ricka. We construct filtered spectrum models for the effective filtration and use these to compute the effective slices.

 If time permits, we will also consider other motivic filtrations such as the one coming from Morel's homotopy t-structure, or Spitzweck-Østvær’s very effective filtration. We will then provide filtered spectrum versions of these filtrations in C-motivic homotopy theory.