Motivic (Representation) Stability of Representation Varieties and Character Stacks

2025/05/11 by Márton Hablicsek, Hablicsek, Márton, Jesse Vogel +1
Mathematics · #14F45 #14M35 #20C05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2505.06879

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties equipped with an action of a finite group G. This motivic decomposition decomposes the virtual class of the variety with respect to irreducible rational representations of G. We also formulate conjectures on motivic representation stability in the context of representation varieties and character stacks, and we verify the conjectures for groups whose virtual classes have been extensively studied.

Citations

• Arithmetic-Geometric Correspondence of Character Stacks via Topological Quantum Field Theory
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Related

• A Survey of Representation Stability Theory
• Motivic homotopy theory of group scheme actions
• Equivariant motivic homotopy theory
• Blocks and support varieties
• Motivic spectral Mackey functors