Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles

2025/09/11 by R. Li, Li, Ruoxi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.09861

openalex publication_date 2025/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a ring of motivic classes of stacks suitable for symmetric powers in finite characteristic. Let X be a smooth projective curve over a field of arbitrary characteristic. We calculate the motivic classes of the moduli stacks of semistable Higgs bundles on X. This recovers results of Fedorov, A. Soibelman and Y. Soibelman in characteristic zero, as well as those of Mozgovoy and Schiffmann for finite fields. We also obtain a simpler formula for the motivic classes of the stacks of Higgs bundles in the universal λ-ring quotient using Mellit's results.

Citations

• Motivic classes of irregular Higgs bundles and irregular connections on a curve
• Poincare polynomials of character varieties, Macdonald polynomials and\n affine Springer fibers
• Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures)
• Indecomposable vector bundles and stable Higgs bundles over smooth projective curves
• Motivic Classes of Commuting Varieties via Power Structures
• The Grothendieck group of algebraic stacks
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Motivic invariants of Artin stacks and 'stack functions'
• Rationality criteria for motivic zeta-functions
• Motivic measures and stable birational geometry
• On the motive of the Hilbert scheme of points on a surface
• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

Related

• An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves
• Motivic mirror symmetry and χ‐independence for Higgs bundles in arbitrary characteristic
• Motivic classes of irregular Higgs bundles and irregular connections on a curve
• Counting Higgs bundles
• On the Voevodsky motive of the moduli space of Higgs bundles on a curve