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H 1 Periods of $1$-motives

Auteurs : Huber-Klawitter, Annette (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : (joint work with G. Wüstholz) Roughly, $1$-dimensional periods are the complex numbers obtained by integrating a differential form on an algebraic curve over $\bar{\mathbf{Q}}$ over a suitable domain of integration. One of the alternative characterisations is as periods of Deligne $1$-motives.
    We clear up the linear relations between these numbers, proving Kontsevich's version of the period conjecture for $1$-dimensional periods. In particular, a $1$-dimensional period is shown to be algebraic if and only if it is of the form $\int_\gamma (\phi+df)$ with $\int_\gamma\phi=0$. We also get formulas for the spaces of periods of a given $1$-motive, generalising Baker's theorem on logarithms of algebraic numbers.
    The proof is based on a version of Wüstholz's analytic subgroup theorem for $1$-motives.

    Keywords : $1$-dimensional period; $1$-motive; Deligne motives; Wüstholz theorem

    Codes MSC :
    14F42 - Motivic cohomology; motivic homotopy theory
    19E15 - Algebraic cycles and motivic cohomology (K-theory)
    19F27 - Étale cohomology, higher regulators, zeta and L-functions (K-theory)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 25/10/2018
      Date de captation : 17/10/2018
      Collection : Research talks
      Format : MP4
      Durée : 01:01:32
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-10-17_Negut.mp4

    Informations sur la rencontre

    Nom de la rencontre : Cohomology of algebraic varieties / Cohomologie des variétés algébriques
    Organisateurs de la rencontre : Cadoret, Anna ; Charles, François ; Demarche, Cyril ; Klinger, Bruno ; Moonen, Ben
    Dates : 15/10/2018 - 19/10/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1775.html

    Citation Data

    DOI : 10.24350/CIRM.V.19467003
    Cite this video as: Huber-Klawitter, Annette (2018). Periods of $1$-motives. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19467003
    URI : http://dx.doi.org/10.24350/CIRM.V.19467003


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