Motivic infinite loop spaces
| Autor: | Vladimir Sosnilo, Maria Yakerson, Adeel A. Khan, Elden Elmanto, Marc Hoyois |
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| Rok vydání: | 2021 |
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Subcategory
Pure mathematics K-Theory and Homology (math.KT) Space (mathematics) Suspension (topology) Mathematics - Algebraic Geometry Morphism Infinite loop Mathematics - K-Theory and Homology FOS: Mathematics Algebraic Topology (math.AT) Perfect field Cotangent complex Mathematics - Algebraic Topology Affine transformation Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Cambridge Journal of Mathematics. 9:431-549 |
| ISSN: | 2168-0949 2168-0930 |
| DOI: | 10.4310/cjm.2021.v9.n2.a3 |
| Popis: | We prove a recognition principle for motivic infinite P1-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 E-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. Comment: 78 pages. v6: final version, to appear in the Cambridge Journal of Mathematics; v5: replace Nisnevich by Zariski; v4: include the case of characteristic 2; v3: fix a mistake in Appendix B and state explicitly the "BPQ" and "framed cobordism" descriptions of the motivic sphere spectrum; v2: generalized the main results to finite fields |
| Databáze: | OpenAIRE |
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