3 citations · 4 across the 6 of their papers we have counts for
8 papers
Abhyankar's conjectures in Galois theory: Current status and future directions
David Harbater, Andrew Obus, Rachel Pries +1
In this paper, we survey the major contributions of Abhyankar to the development of the theory of fundamental groups and Galois covers in positive characteristic. We first discuss…
Subgroups of profinite surface groups
Lior Bary-Soroker, Katherine F. Stevenson, Pavel Zalesskii
We study the subgroup structure of the étale fundamental group of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond…
Normal subgroups of fundamental groups of affine curves in positive characteristic II
Amilcar Pacheco, Pavel Zalesskii, Katherine F. Stevenson
Let be an algebraically closed field of characteristic and let be a smooth connected affine curve. Denote by its algebraic fundamental group. The goal of t…
A survey of Galois theory of curves in characteristic p
Rachel Pries, Katherine Stevenson
This survey is about Galois theory of curves in characteristic p, a topic which has inspired major research in algebraic geometry and number theory and which contains many open que…
Embedding problems and open subgroups
David Harbater, Katherine F. Stevenson
We study the properties of the fundamental group of an affine curve over an algebraically closed field of characteristic , from the point of view of embedding problems. In chara…
Semi-direct Galois covers of the affine line
Linda Gruendken, Laura Hall-Seelig, Bo-Hae Im +3
Let be an algebraically closed field of characteristic . Let be semi-direct product where is a prime distinct from . In this paper, we stud…
Local Galois theory in dimension two: Second edition
David Harbater, Katherine F. Stevenson
We prove a generalization of Shafarevich's Conjecture for fields of Laurent series in two variables over an arbitrary field. While not projective, the absolute Galois group of such…
Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic
Amilcar Pacheco, Pavel Zalesski, Katherine F. Stevenson
Let be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic of countable cardinality. Let…