  To an Adams-type homology theory we associate a notion of a synthetic
spectrum, this is a product-preserving sheaf on the site of finite spectra with
projective $E$-homology. We prove that the $\infty$-category $Syn_{E}$ of
synthetic spectra based on $E$ is in a precise sense a deformation of the
$\infty$-category of spectra into quasi-coherent sheaves over a certain
algebraic stack, and show that this deformation encodes the $E$-based Adams
spectral sequence.
  We describe a symmetric monoidal functor from cellular motivic spectra over
the complex numbers into an even variant of synthetic spectra based on $MU$ and
show that it induces an equivalence between the $\infty$-categories of
$p$-complete objects for all primes $p$. In particular, it follows that the
$p$-complete cellular motivic category can be described purely in terms of
chromatic homotopy theory.
