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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Veröffentlicht in:Bulletin (new series) of the American Mathematical Society 2018-04, Vol.55 (2), p.239-287
Hauptverfasser: Harbater, David, Obus, Andrew, Pries, Rachel, Stevenson, Katherine
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Stevenson, Katherine
description 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.
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source American Mathematical Society Publications (Freely Accessible); Project Euclid Open Access; American Mathematical Society Publications
subjects Decomposition
Inertia
Theorems
Theory
Topology
title Abhyankar's conjectures in Galois theory: Current status and future directions
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