# Modules over algebraic cobordism

@article{Elmanto2020ModulesOA,
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},
year={2020},
volume={8}
}
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
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