2023/01/03 by David A. Nadler, Vivek Shende, Nadler, David +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2301.01342
openalex publication_date 2023/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spectral side of the (conjectural) Betti geometric Langlands correspondence concerns sheaves on the character stack of an algebraic curve; in particular, the categories in question are manifestly invariant under deformations of the curve. By contrast the same invariance is certainly not manifest, and is presently not known, for their automorphic counterparts, in particular because the singularities of the global nilpotent cone may vary significantly with the complex structure of the curve. Here we establish the corresponding invariance statement for the category of microsheaves on the open subset of stable Higgs bundles on nonstacky components where all semistables are stable, e.g. for coprime rank and degree or for a punctured curve with generic parabolic weights. The proof uses the known global symplectic geometry of the Higgs moduli space to invoke recent results on the invariance of microlocal sheaves.