Mixed Hodge structures and representations of fundamental groups of algebraic varieties
| Autor: | Louis-Clément Lefèvre |
|---|---|
| Přispěvatelé: | Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-16-CE40-0011,Hodgefun,Groupes fondamentaux, Théorie de Hodge et Motifs(2016), Institut Fourier ( IF ), Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), ANR-16-CE40-0011-01,Hodgefun,Fundamental Groups, Hodge Theory and Motives, Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
L-infinity algebras
Complex algebraic geometry Pure mathematics Fundamental group General Mathematics 01 natural sciences Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics Hodge theory Representation varieties 0101 mathematics Algebraic Geometry (math.AG) Mathematics Formal deformation theory Linear algebraic group MSC: 14C30 14D15 14D07 18D50 010102 general mathematics Local ring Algebraic variety [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG] Monodromy Fundamental groups Mathematik 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Variety (universal algebra) Hodge structure |
| Zdroj: | Advances in Mathematics Advances in Mathematics, Elsevier, 2019, 349, pp.869-910. ⟨10.1016/j.aim.2019.04.028⟩ IF_PREPUB. 34 pages. 2018 |
| ISSN: | 0001-8708 1090-2082 |
| DOI: | 10.1016/j.aim.2019.04.028⟩ |
| Popis: | 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 Hodgediagrams and methods of $L\_\infty$ algebras. We apply it in two geometric situations: either when $X$ is compact K{\"a}hler and $\rho$ is the monodromy of a variation of Hodge structure, or when $X$ is smooth quasi-projective and $\rho$ has finite image. Comment: 34 pages |
| Databáze: | OpenAIRE |
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