Meromorphic Hodge Moduli Spaces for Reductive Groups in Arbitrary Characteristic
Abstract
Fix a smooth projective family of curves C→S and a split reductive group scheme G over a Noetherian base scheme S. For any (possibly nonreduced) fixed relative Cartier divisor D, we provide a treatment of the moduli of G-bundles on the fibers of C equipped with t-connections with pole orders bounded by D. Under mild assumptions on the characteristics of all the residue fields of S, we construct a Hodge moduli space MHod,G→AS1 for the semistable locus, construct a Harder–Narasimhan stratification, and thus obtain a semistable reduction theorem. If all the fibers of the divisor of poles D are nonempty, then we show that the stack of semistable objects is smooth over AS1. We also define a Hodge–Hitchin morphism in positive characteristic and prove that it is proper.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometry and complex manifolds
Publication details
- Journal / source
- The Michigan Mathematical Journal
- Publisher
- Michigan Mathematical Journal
- Volume
- -1
- Issue
- -1
- Pages
- 1-62
- Publication date
- 1 January 2026
- Language
- EN