English

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

Algebraic Geometry 2018-07-25 v2 Number Theory

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.

Keywords

Cite

@article{arxiv.1408.0859,
  title  = {Abhyankar's conjectures in Galois theory: Current status and future directions},
  author = {David Harbater and Andrew Obus and Rachel Pries and Katherine Stevenson},
  journal= {arXiv preprint arXiv:1408.0859},
  year   = {2018}
}

Comments

Final version, 47 pp. To appear in Bull. Amer. Math. Soc