2023/08/25 by Davesh Maulik, Maulik, Davesh, Junliang Shen +3 · 8 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2308.13160
openalex publication_date 2023/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the interaction between Fourier-Mukai transforms and perverse filtrations for a certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the "Perverse ⊃ Chern" phenomenon for these abelian fibrations are immediate consequences of our theory. We also show that our class of fibrations include families of compactified Jacobians of integral locally planar curves. Applications include the following: (a) we prove the motivic decomposition conjecture for this class (including compactified Jacobian fibrations), which generalizes Deninger-Murre's theorem for abelian schemes; (b) we provide a new proof of the P=W conjecture for GLr; (c) we prove half of the P=C conjecture concerning refined BPS invariants for the local ℙ2; (d) we show that the perverse filtration for the compactified Jacobian associated with an integral locally planar curve is multiplicative, which generalizes a result of Oblomkov-Yun for homogeneous singularities. Our techniques combine Arinkin's autoduality for coherent categories, Ngô's support theorem for the decomposition theorem, Adams operations in operational K-theory, and Corti-Hanamura's theory of relative Chow motives.