Arithmetic geometry & number theory
Research
I study Galois covers of curves in characteristic p, with an emphasis on wild ramification, deformation, and liftability to characteristic zero. More recently, I have been exploring p-adic differential equations as a way to understand degenerations of wildly ramified covers.
Publications & preprints
Ten projects, newest first.
10With Yuri Yatagawa · in preparation
The lifting problem and Brylinski’s filtration in mixed characteristic
We construct Witt-type vectors from Kummer data, derive an explicit Swan-conductor formula, and formulate a mixed-characteristic analogue of Brylinski’s filtration.
With Nguyen-Dang Khai-Hoan · submitted, 2024
Kummer–Artin–Schreier–Witt theory
An algebrization of Matsuda’s morphism connecting the Kummer and Artin–Schreier–Witt exact sequences of group schemes.
Algebraic Geometry 13 (2026), 305–370 · DOI: 10.14231/AG-2026-010
Deforming cyclic covers in towers
A deformation of a cyclic subcover in positive characteristic can be extended through the entire tower after a finite base extension.
Annales de l’Institut Fourier · to appear
Hurwitz trees and deformations of Artin–Schreier covers
Generalized Hurwitz trees classify deformation types and give new information about connectedness in moduli.
With S. Groen · Journal of Number Theory 279 (2026), 78–116 · DOI: 10.1016/j.jnt.2025.05.016
a-numbers of ℤ/p²-covers of the projective line
We identify a family of ℤ/9-covers whose a-numbers are determined by the ramification data.
With Matthias Hippold · IMRN 2024, 10169–10188 · DOI: 10.1093/imrn/rnae060
The moduli space of cyclic covers in positive characteristic
We identify the irreducible components of the moduli space, determine their dimensions, and study deformations varying p-rank and branch points.
Preprint, 2024
The vanishing of the Hurwitz tree obstruction for the refined local lifting problem
We introduce Hurwitz-tree obstructions for the refined local lifting problem and determine when they vanish for cyclic groups.
Preprint, 2021
The refined lifting problem for cyclic coverings of order 4
We show that ℤ/4-covers in characteristic 2 lift in towers when the first-level lift satisfies a suitable condition.
With S. Das, K. Karagiannis, A. Obus, and V. Thatte · JTNB 34 (2022), 251–269 · DOI: 10.5802/jtnb.1200
Local Oort groups and the isolated differential data criterion
The isolated differential data criterion proves new lifting results for covers with specified dihedral inertia groups.
Journal of Algebra 547 (2020), 398–429 · DOI: 10.1016/j.jalgebra.2019.11.034
Connectedness of the moduli space of Artin–Schreier curves of fixed genus
The moduli space of Artin–Schreier covers of the projective line of genus g is connected when g is sufficiently large.