Tom Bachmann ; Elden Elmanto ; Marc Hoyois ; Adeel A. Khan ; Vladimir Sosnilo et al. - On the infinite loop spaces of algebraic cobordism and the motivic sphere

epiga:6581 - Épijournal de Géométrie Algébrique, May 19, 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.volume5.6581
On the infinite loop spaces of algebraic cobordism and the motivic sphereArticle

Authors: Tom Bachmann ; Elden Elmanto ; Marc Hoyois ; Adeel A. Khan ; Vladimir Sosnilo ; Maria Yakerson

    We obtain geometric models for the infinite loop spaces of the motivic spectra $\mathrm{MGL}$, $\mathrm{MSL}$, and $\mathbf{1}$ over a field. They are motivically equivalent to $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{lci}(\mathbb{A}^\infty)^+$, $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{or}(\mathbb{A}^\infty)^+$, and $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{fr}(\mathbb{A}^\infty)^+$, respectively, where $\mathrm{Hilb}_d^\mathrm{lci}(\mathbb{A}^n)$ (resp. $\mathrm{Hilb}_d^\mathrm{or}(\mathbb{A}^n)$, $\mathrm{Hilb}_d^\mathrm{fr}(\mathbb{A}^n)$) is the Hilbert scheme of lci points (resp. oriented points, framed points) of degree $d$ in $\mathbb{A}^n$, and $+$ is Quillen's plus construction. Moreover, we show that the plus construction is redundant in positive characteristic.


    Volume: Volume 5
    Published on: May 19, 2021
    Accepted on: May 19, 2021
    Submitted on: June 19, 2020
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Algebraic Topology,Mathematics - K-Theory and Homology
    Funding:
      Source : OpenAIRE Graph
    • Incentive - LA 1 - 2013; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: Incentivo/SAU/LA0001/2013

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