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H 1 Mixed motives associated to elliptic curves

Auteurs : Hain, Richard (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The absolute Galois group of the rational numbers acts on the various flavours (profinite, prounipotent, pro-$\ell$) of the fundamental group of a smooth projective curve over the rationals. The image of the corresponding homomorphism normalizes the image of the profinite mapping class group in the automorphism group of the geometric fundamental group of the curve. The image of the Galois action modulo these “geometric automorphisms” is independent of the curve. A basic problem is to determine this image. This talk is a report on a joint project with Francis Brown whose goal is to understand the image mod geometric automorphisms in the prounipotent case. Standard arguments reduce the problem to one in genus 1, where one can approach the problem by studying the periods of iterated integrals of modular forms and their relation to multiple zeta values.

    Codes MSC :
    14H30 - Coverings, fundamental group (curves)
    14H52 - Elliptic curves
    11M32 - Multiple Dirichlet series and zeta functions and multizeta values

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 02/12/15
      Date de captation : 27/10/15
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 01:03:29
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-10-27_Hain.mp4

    Informations sur la rencontre

    Nom de la rencontre : Moduli spaces in geometry / Espaces de modules en géométrie
    Organisateurs de la rencontre : Ayoub, Joseph ; Schmitt, Alexander ; Teleman, Andrei
    Dates : 26/10/15 - 30/10/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1139.html

    Citation Data

    DOI : 10.24350/CIRM.V.18870303
    Cite this video as: Hain, Richard (2015). Mixed motives associated to elliptic curves. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18870303
    URI : http://dx.doi.org/10.24350/CIRM.V.18870303


    Bibliographie

    1. Brown, F. (2014). Multiple Modular Values for $SL_2(\mathbb{Z})$. - http://arxiv.org/abs/1407.5167

    2. Hain, R. (2015). The Hodge-de Rham Theory of Modular Groups. - http://arxiv.org/abs/1403.6443

    3. Hain, R., & Matsumoto, M. Universal mixed elliptic motives. To be appeared -

    4. Manin, Yuri I. (2005). Iterated Shimura integrals. Moscow Mathematical Journal, 5(4), 869-881 - http://www.ams.org/distribution/mmj/vol5-4-2005/manin.pdf

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