The Hodge theory of character varieties

2010/11/03 by Mark Andrea de Cataldo, de Cataldo, Mark Andrea
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1011.0784

openalex publication_date 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a report on joint work with T. Hausel and L. Migliorini, where we prove, for each of the groups GL(2,C), PGL(2,C), SL(2,C), that the non-Abelian Hodge theorem identifies the weight filtration on the cohomology of the character variety with the perverse Leray filtration on the cohomology of the domain of the Hitchin map. We review the decomposition theorem, Nĝo's support theorem, the geometric description of the perverse filtration and the sub-additivity of the Leray filtration with respect to the cup product.

Related

• Topology of Hitchin systems and Hodge theory of character varieties: the case A₁
• The Hodge filtration on nonabelian cohomology
• The perverse filtration for the Hitchin fibration is locally constant
• Filtrations on the Chow groups and transcendence degree
• Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve