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H 1 Crystalline cohomology, period maps, and applications to K3 surfaces

Auteurs : Liedtke, Christian (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will first introduce K3 surfaces and determine their algebraic deRham cohomology. Next, we will see that crystalline cohomology (no prior knowledge assumed) is the "right" replacement for singular cohomology in positive characteristic. Then, we will look at one particular class of K3 surfaces more closely, namely, supersingular K3 surfaces. These have Picard rank 22 (note: in characteristic zero, at most rank 20 is possible) and form 9-dimensional moduli spaces. For supersingular K3 surfaces, we will see that there exists a period map and a Torelli theorem in terms of crystalline cohomology. As an application of the crystalline Torelli theorem, we will show that a K3 surface is supersingular if and only if it is unirational.

    Codes MSC :
    14D22 - Fine and coarse moduli spaces
    14J28 - $K3$ surfaces and Enriques surfaces
    14M20 - Rational and unirational varieties
    14G17 - Positive characteristic ground fields

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 20/09/16
      Date de captation : 13/09/16
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 00:54:02
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-09-13_Liedtke.mp4

    Informations sur la rencontre

    Nom de la rencontre : Higher dimensional algebraic geometry and characteristic p > 0 / Géométrie algébrique en dimension supérieure et caractéristique p > 0
    Organisateurs de la rencontre : Blickle, Manuel ; Schwede, Karl ; Xu, Chenyang
    Dates : 12/09/16 - 16/09/16
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1376.html

    Citation Data

    DOI : 10.24350/CIRM.V.19049303
    Cite this video as: Liedtke, Christian (2016). Crystalline cohomology, period maps, and applications to K3 surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19049303
    URI : http://dx.doi.org/10.24350/CIRM.V.19049303


    Voir aussi

    Bibliographie

    1. Liedtke, C. (2016). Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem. - https://arxiv.org/abs/1403.2538

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