Elmanto, Elden and Hoyois, Marc and Khan, Adeel A. and Sosnilo, Vladimir and Yakerson, Maria (2020) Modules over algebraic cobordism. FORUM OF MATHEMATICS PI, 8: e14. ISSN 2050-5086,
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We prove that the infinity-category of MGL-modules over any scheme is equivalent to the infinity-category of motivic spectra with finite syntomic transfers. Using the recognition principle for infinite P-1-loop spaces, we deduce that very effective 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 nonnegative rank in terms of the moduli stack of finite quasi-smooth derived schemes with the corresponding tangential structure. In particular, over a regular equicharacteristic base, we show that Omega(infinity)(P1) MGL is the A(1)-homotopy type of the moduli stack of virtual finite flat local complete intersections, and that for n > 0, Omega(infinity)(P1) Sigma(n)(P1) MGL is the A(1)-homotopy type of the moduli stack of finite quasi-smooth derived schemes of virtual dimension -n.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Mar 2021 13:38 |
| Last Modified: | 04 Mar 2021 13:38 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43124 |
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