Non-abelian Hodge moduli spaces and homogeneous affine Springer fibers

2022/09/29 by Roman Bezrukavnikov, Pablo Boixeda Alvarez, Bezrukavnikov, Roman +5 · 2 citations
Mathematics · #14D24 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14D20 #Representation Theory (math.RT) #Secondary 14M15

paper · pdf · doi:10.48550/arxiv.2209.14695

openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Starting from a homogeneous affine Springer fiber Fl_ψ, we construct three moduli spaces that correspond to the Dolbeault, de Rham and Betti aspects of a hypothetical Simpson correspondence with wild ramifications. We show that Fl_ψ is homeomorphic to the central Lagrangian fiber in the Dolbeault space, prove that the Dolbeaut and de Rham spaces both have the same cohomology as Fl_ψ, and construct a map from the de Rham space to the Betti space which we conjecture to be an analytic isomorphism.

Cited by

• Cohomology of compactified Jacobians for locally planar integral curves
• An explicit local geometric Langlands for supercuspidal representations: the toral case

Related

• Moduli spaces in p-adic non-abelian Hodge theory
• P=W phenomena on abelian varieties
• Homology of affine Springer fibers in the unramified case
• Generalized affine Springer fibers
• Rigid analytic p-adic Simpson correspondence for line bundles