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H 1 Representation varieties of fundamental groups of complex algebraic varieties and mixed Hodge structures

Auteurs : Lefèvre, Louis-Clément (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We study locally the representation varieties of fundamental groups of smooth complex algebraic varieties. These are schemes whose complex points parametrize such representations into linear algebraic groups. At a given representation, the structure of the formal local ring to the representation variety tells about the obstructions to deform formally this representation, which is ultimately related to topological obstructions to the possible fundamental groups of complex algebraic varieties. This was first described by Goldman and Millson in the case of compact Kähler manifold, using formal deformation theory and differential graded Lie algebras. We review this using methods of Hodge theory and of derived deformation theory and we are able to describe locally the representation variety for non-compact smooth varieties and representations underlying a variation of Hodge structure.

    Keywords : deformation theory, fundamental groups, representation varieties, L-infinity algebras, mixed Hodge modules, variations of Hodge structure

    Codes MSC :
    14C30 - Transcendental methods, Hodge theory, Hodge conjecture
    14D07 - Variation of Hodge structures
    14D15 - Formal methods; deformations, See also {13D10, 14B07, 16S80, 32Gxx}
    18D50 - Operads

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 17/12/2019
      Date de captation : 28/11/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:52:32
      Domaine : Algebraic & Complex Geometry ; Topology
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-11-28_Lefevre.mp4

    Informations sur la rencontre

    Nom de la rencontre : Algebraic Geometry and Complex Geometry / Géométrie algébrique et géométrie complexe
    Organisateurs de la rencontre : Benoist, Olivier ; Floris, Enrica
    Dates : 25/11/2019 - 29/11/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2074.html

    Citation Data

    DOI : 10.24350/CIRM.V.19581103
    Cite this video as: Lefèvre, Louis-Clément (2019). Representation varieties of fundamental groups of complex algebraic varieties and mixed Hodge structures. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19581103
    URI : http://dx.doi.org/10.24350/CIRM.V.19581103


    Voir aussi

    Bibliographie

    1. LEFÈVRE, Louis-Clément. Mixed Hodge structures and representations of fundamental groups of algebraic varieties. Advances in Mathematics, 2019, vol. 349, p. 869-910. - https://arxiv.org/abs/1806.02688

    2. LEFÈVRE, Louis-Clément. Deformations of representations of fundamental groups of non-compact complex varieties. arXiv preprint arXiv: 1912.04787, 2019. - https://arxiv.org/abs/1912.04787

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