Modules over algebraic cobordism

  title={Modules over algebraic cobordism},
  author={E. Elmanto and Marc Hoyois and Adeel A. Khan and Vladimir A. Sosnilo and Maria Yakerson},
  journal={Forum of Mathematics, Pi},
Abstract We prove that the $\infty $-category of $\mathrm{MGL} $-modules over any scheme is equivalent to the $\infty $-category of motivic spectra with finite syntomic transfers. Using the recognition principle for infinite $\mathbf{P} ^1$-loop spaces, we deduce that very effective $\mathrm{MGL} $-modules over a perfect field are equivalent to grouplike motivic spaces with finite syntomic transfers. Along the way, we describe any motivic Thom spectrum built from virtual vector bundles of… Expand