# Motivic infinite loop spaces

@article{Elmanto2021MotivicIL,
title={Motivic infinite loop spaces},
author={Elden Elmanto and Marc Hoyois and Adeel A. Khan and Vladimir A. Sosnilo and Maria Yakerson},
journal={Cambridge Journal of Mathematics},
year={2021}
}
• Published 14 November 2017
• Mathematics
• Cambridge Journal of Mathematics
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…
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We relate the recognition principle for infinite P1 ‐loop spaces to the theory of motivic fundamental classes of Déglise, Jin and Khan. We first compare two kinds of transfers that are naturally
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