We describe how to any Adams-type homology theory \(E\) one can associate a homotopy theory of so called synthetic spectra based on \(E\), this is in a precise sense a deformation of Hovey's homotopy theory of comodules whose generic fibre is given by the homotopy theory of spectra.
We discuss how the even variant of this construction based on \(MU\) is equivalent to the homotopy theory of cellular complex motivic spectra after \(p\)-completion at any prime \(p\).
This talk is expository in nature and all the needed notions will be introduced.