Abhyankar’s conjectures in Galois theory: current status and future directions. (English) Zbl 1432.14029
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.
MSC:
| 14H30 | Coverings of curves, fundamental group |
| 11G20 | Curves over finite and local fields |
| 14H37 | Automorphisms of curves |
| 11-02 | Research exposition (monographs, survey articles) pertaining to number theory |
| 14-02 | Research exposition (monographs, survey articles) pertaining to algebraic geometry |
| 12F10 | Separable extensions, Galois theory |
Keywords:
Abhyankar conjecture; Galois cover; fundamental group; ramification theory; lifting problem; finite characteristicReferences:
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