Forum of Mathematics, Pi (Jan 2020)

Modules over algebraic cobordism

  • Elden Elmanto,
  • Marc Hoyois,
  • Adeel A. Khan,
  • Vladimir Sosnilo,
  • Maria Yakerson

DOI
https://doi.org/10.1017/fmp.2020.13
Journal volume & issue
Vol. 8

Abstract

Read online

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.

Keywords