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H 1 A Jacobian criterion for smoothness of algebraic diamonds

Auteurs : Fargues, Laurent (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : (joint work with Peter Scholze) In our joint work with Scholze we need to give a meaning to statements like "the stack of principal G-bundles on the curve is smooth of dimension 0" and construct "smooth perfectoid charts on it". The problem is that in the perfectoid world there is no infinitesimals and thus no Jacobian criterion that would allow us to define what is a smooth morphism. The good notion in this setting is the one of a cohomologically smooth morphism, a morphism that satisfies relative Poincaré duality. I will explain a Jacobian criterion of cohomological smoothness for moduli spaces of sections of smooth algebraic varieties over the curve that allows us to solve our problems.

    Codes MSC :
    11F85 - $p$-adic theory, local fields
    11R39 - Langlands-Weil conjectures, nonabelian class field theory
    11S31 - Class field theory for local fields; $p$-adic formal groups
    14G22 - Rigid analytic geometry
    14H40 - Jacobians, Prym varieties

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 10/07/2018
      Date de captation : 03/07/2018
      Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory
      Format : MP4
      Durée : 01:10:43
      Domaine : Algebraic & Complex Geometry ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-07-03_Fargues.mp4

    Informations sur la rencontre

    Nom de la rencontre : $p$-adic Langlands correspondence, Shimura varieties and perfectoids / Correspondance de Langlands $p$-adique, variétés de Shimura et perfectoïdes
    Organisateurs de la rencontre : Boyer, Pascal ; Colmez, Pierre ; Hida, Haruzo ; Pilloni, Vincent ; Rapoport, Michael
    Dates : 02/07/2018 - 06/07/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1649.html

    Citation Data

    DOI : 10.24350/CIRM.V.19418903
    Cite this video as: Fargues, Laurent (2018). A Jacobian criterion for smoothness of algebraic diamonds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19418903
    URI : http://dx.doi.org/10.24350/CIRM.V.19418903


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