Abhyankar's conjectures in Galois theory: Current status and future directions

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 the current status of four conjectures of Abhyankar about Galois covers in positive characteristic. Then we discuss resea...

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Published inBulletin (new series) of the American Mathematical Society Vol. 55; no. 2; pp. 239 - 287
Main Authors Harbater, David, Obus, Andrew, Pries, Rachel, Stevenson, Katherine
Format Journal Article
LanguageEnglish
Published Providence American Mathematical Society 01.04.2018
Subjects
Decomposition
Inertia
Theorems
Theory
Topology
Galois cover
ramification theory
fundamental group
finite characteristic
Abhyankar conjecture
lifting problem
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Summary: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 the current status of four conjectures of Abhyankar about Galois covers in positive characteristic. Then we discuss research directions inspired by Abhyankar's work, including many open problems.
ISSN:0273-0979
1088-9485
DOI:10.1090/bull/1594