Elmanto, Elden and Hoyois, Marc and Khan, Adeel A. and Sosnilo, Vladimir and Yakerson, Maria (2021) Motivic infinite loop spaces. CAMBRIDGE JOURNAL OF MATHEMATICS, 9 (2). pp. 431-549. ISSN 2168-0930, 2168-0949
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We prove a recognition principle for motivic infinite P-1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of epsilon(infinity)-spaces. A framed motivic space is a motivic space equipped with transfers along finite syntomic morphisms with trivialized cotangent complex in K-theory. Our main result is that grouplike framed motivic spaces are equivalent to the full subcategory of motivic spectra generated under colimits by suspension spectra. As a consequence, we deduce some representability results for suspension spectra of smooth varieties, and in particular for the motivic sphere spectrum, in terms of Hilbert schemes of points in affine spaces.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | K-THEORY; DESCENT; FUNCTORS; Motivic Stable Homotopy Theory; Infinite Loop Space Theory; Recognition Principle; Cotangent Complex |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Sep 2022 08:36 |
| Last Modified: | 16 Sep 2022 08:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/47528 |
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