Mixed Hodge structures and representations of fundamental groups of algebraic varieties - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2019

Mixed Hodge structures and representations of fundamental groups of algebraic varieties

Louis-Clément Lefèvre

Résumé

Given a complex variety $X$, a linear algebraic group $G$ and a representation $\rho$ of the fundamental group $\pi_1(X,x)$ into $G$, we develop a framework for constructing a functorial mixed Hodge structure on the formal local ring of the representation variety of $\pi_1(X,x)$ into $G$ at $\rho$ using mixed Hodge diagrams and methods of $L_\infty$ algebras. We apply it in two geometric situations: either when $X$ is compact Kähler and $\rho$ is the monodromy of a variation of Hodge structure, or when $X$ is smooth quasi-projective and $\rho$ has finite image.
Fichier principal
Vignette du fichier
Article.pdf (422.67 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01809625 , version 1 (06-06-2018)

Identifiants

Citer

Louis-Clément Lefèvre. Mixed Hodge structures and representations of fundamental groups of algebraic varieties. Advances in Mathematics, 2019, 349, pp.869-910. ⟨10.1016/j.aim.2019.04.028⟩. ⟨hal-01809625⟩
178 Consultations
115 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More