Publications
Published work and papers to appear, newest first.
Hurwitz trees and deformations of Artin–Schreier covers
Generalized Hurwitz trees classify deformation types and give new information about connectedness in moduli.
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.
Research papers
Preprints
On lifting representations and actions on curves of the metacyclic groups Cₚˢ ⋊ Cₘ
We give criteria for lifting representations of metacyclic groups and apply them to actions on curves, including an obstruction to lifting in mixed characteristic.
Kummer–Artin–Schreier–Witt theory
An algebrization of Matsuda’s morphism connecting the Kummer and Artin–Schreier–Witt exact sequences of group schemes.
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.
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.