Motivic infinite loop spaces
By E. Elmanto, Marc Hoyois, Adeel A. Khan, V. Sosnilo, Maria Yakerson. Cambridge Journal of Mathematics, 2017
48 citations recorded by the source corpus.
We prove a recognition principle for motivic infinite P1-loop spaces over an infinite 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d2cb3f6d614e2828b29cdc21897930302cb66f74
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In Geometry and Topology
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Citations in the corpus
- Fundamental classes in motivic homotopy theory (2018, background): “It is proven in [EHK17] that this structure can be used to recognize infinite P(1)-loop spaces, in the same way that E∞-structures can be used to recognize infinite loop spaces in topology (see also [GP18]).”