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Motivic infinite loop spaces

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arxiv 1711.05248 v6 pith:Q4YKQRBM submitted 2017-11-14 math.AG math.ATmath.KT

classification math.AGmath.ATmath.KT
keywords motivicspacesframedspectrainfinitespacesuspensiontheory
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modules over algebraic cobordism

    math.AG 2019-08 accept novelty 8.0 of 10

    MGL-modules over a scheme are equivalent to motivic spectra with finite syntomic transfers, and the infinite P^1-loop space of MGL is the A^1-homotopy type of the moduli stack of finite syntomic schemes.

  2. The unit map of the algebraic special linear cobordism spectrum

    math.KT 2019-08 accept novelty 6.0 of 10

    Over characteristic 0 fields, the unit map from the motivic sphere spectrum to the special linear cobordism spectrum MSL is an isomorphism on homotopy modules, proven by comparing framed and SL-oriented framed corresp...

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