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

Harbater, David; Obus, Andrew; Pries, Rachel; Stevenson, Katherine

doi:10.1090/bull/1594

Abhyankar’s conjectures in Galois theory: Current status and future directions
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by David Harbater, Andrew Obus, Rachel Pries and Katherine Stevenson PDF

Bull. Amer. Math. Soc. 55 (2018), 239-287 Request permission

Abstract:

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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