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H 1 The rational motivic sphere spectrum and motivic Serre finiteness

Auteurs : Levine, Marc (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : After inverting 2, the motivic sphere spectrum splits into a plus part and a minus part with respect to a certain natural involution. Cisinsky and Déglise have shown that, with rational coefficients, the plus part is given by rational motivic cohomlogy. With Ananyevskiy and Panin, we have computed the minus part with rational coefficients as being given by rational Witt-theory. In particular, this shows that the rational bi-graded homotopy sheaves of the minus sphere are concentrated in bi-degree (n,n). This may be rephrased as saying that the graded homotopy sheaves of the minus sphere in strictly positive topological degree are torsion. Combined with the result of Cisinski-Déglise mentioned above, this shows that the graded homotopy sheaves of the sphere spectrum in strictly positive topological degree and non-negative Tate degree are torsion, an analog of the classical theorem of Serre, that the stable homotopy groups of spheres in strictly positive degree are finite.

    Codes MSC :
    14C25 - Algebraic cycles
    14F42 - Motivic cohomology; motivic homotopy theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 29/09/2015
      Date de captation : 02/09/2015
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      arXiv category : Algebraic Geometry ; Algebraic Topology
      Domaine : Algebraic & Complex Geometry ; Topology
      Durée : 01:06:48
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-09-02_Levine.mp4

    Informations sur la rencontre

    Nom de la rencontre : Cohomological Methods in the Theory of Algebraic Groups
    Organisateurs de la rencontre : Calmes, Baptiste ; Chernousov, Vladimir ; Karpenko, Nikita
    Dates : 31/08/2015 - 04/09/2015
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1001.html

    Citation Data

    DOI : 10.24350/CIRM.V.18825103
    Cite this video as: Levine, Marc (2015). The rational motivic sphere spectrum and motivic Serre finiteness. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18825103
    URI : http://dx.doi.org/10.24350/CIRM.V.18825103

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