Structures de Hodge mixtes sur les idéaux de saut de cohomologie
| Autor: | Lefèvre, Louis-Clément |
|---|---|
| Přispěvatelé: | Universität Duisburg-Essen [Essen], ANR-16-CE40-0011,Hodgefun,Groupes fondamentaux, Théorie de Hodge et Motifs(2016) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
L-infinity Algebras
Mixed Hodge Structures Homotopy Transfer of Structure idéaux de saut Mathematics - Algebraic Geometry structures de Hodge mixte transfert de structure homotopique Mathematics::Algebraic Geometry algèbres L-infini Jump Ideals [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] 14F35 14D15 14C30 18D50 FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology MSC: 14F35 14D15 14C30 18D50 [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Algebraic Geometry (math.AG) |
| Popis: | In previous work, we constructed for a smooth complex variety $X$ and for a linear algebraic group $G$ a mixed Hodge structure on the complete local ring $\widehat{\mathcal{O}}_\rho$ to the moduli space of representations of the fundamental group $\pi_1(X,x)$ into $G$ at a representation $\rho$ underlying a variation of mixed Hodge structure. We now show that the jump ideals $J_k^i \subset \widehat{\mathcal{O}}_\rho$, defining the locus of representations such the the dimension of the cohomology of $X$ in degree $i$ of the associated local system is greater than $k$, are sub-mixed Hodge structures; this is in accordance with various known motivicity results for these loci. In rank one we also recover, and find new cases, where these loci are translated sub-tori of the moduli of representations. Our methods are first transcendental, relying on Hodge theory, and then combined with tools of homotopy and algebra. Comment: 18 pages, comments are welcome! |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|