Motivic infinite loop spaces
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Author / Producer
Date
2021
Publication Type
Journal Article
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yes
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Abstract
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.
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Publication status
published
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Journal / series
Volume
9 (2)
Pages / Article No.
431 - 549
Publisher
International Press
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Edition / version
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Software
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Date collected
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Subject
Motivic Stable Homotopy Theory; Infinite Loop Space Theory; Recognition Principle; Cotangent Complex
Organisational unit
02500 - Forschungsinstitut für Mathematik / Institute for Mathematical Research