Frobenius induced morphisms on moduli of sheaves on curves

2025/08/30 by Cao, Jin, Su, Xiaoyu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.00444

Abstract

We show the Frobenius pullback of a general semi-stable vector bundle in the moduli space of vector bundles with fixed rank and degree is still semi-stable by the dimension estimate. Then we give various applications of the main theorem.

Citations

• Meromorphic Hodge moduli spaces for reductive groups in arbitrary characteristic
• Moduli of unstable bundles of HN-length two with fixed algebra of endomorphisms
• Moduli spaces of semistable modules over Lie algebroids
• A Cohomological Non Abelian Hodge Theorem in Positive Characteristic
• Projective Completion of Moduli of t-Connections on Curves in Positive and Mixed Characteristic
• Indecomposable vector bundles and stable Higgs bundles over smooth projective curves
• Non-abelian Hodge theory for algebraic curves in characteristic p
• Moduli of flat connections in positive characteristic
• Schematic Harder-Narasimhan Stratification
• Iterated destabilizing modifications for vector bundles with connection
• The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic
• Semistability of Frobenius direct images over curves
• A smooth counterexample to Nori's conjecture on the fundamental group scheme
• Semistable reduction for G-bundles on curves
• The generalized Verschiebung map for curves of genus 2
• Frobenius-unstable bundles and p-curvature
• On Frobenius-destabilized rank-2 vector bundles over curves
• On vector bundles destabilized by Frobenius pull-back
• Localization of modules for a semisimple Lie algebra in prime characteristic
• On the Hitchin morphism in positive characteristic
• The action of the Frobenius map on rank 2 vector bundles in characteristic 2
• The Hodge filtration on nonabelian cohomology
• The Self-Duality Equations on a Riemann Surface

Related

• Frobenius pull-back and stability of vector bundles in characteristic 2
• Frobenius morphism and semi-stable bundles
• Frobenius inverse image of the semi-stable boundary in the moduli space of vector bundles
• On vector bundles destabilized by Frobenius pull-back
• Frobenius Stratification of Moduli Spaces of Vector Bundles in Positive characteristic. II