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

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
Format: Artikel
Sprache:eng
Schlagworte:
Decomposition
Inertia
Theorems
Theory
Topology
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Zusammenfassung: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