Abhyankar’s conjectures in Galois theory: Current status and future directions
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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.References
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Additional Information
- David Harbater
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
- MR Author ID: 205795
- ORCID: 0000-0003-4693-1049
- Email: harbater@math.upenn.edu
- Andrew Obus
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 890287
- ORCID: 0000-0003-2358-4726
- Email: obus@virginia.edu
- Rachel Pries
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- MR Author ID: 665775
- Email: pries@math.colostate.edu
- Katherine Stevenson
- Affiliation: Department of Mathematics, California State Northridge, Northridge, California 91330
- MR Author ID: 608718
- Email: katherine.stevenson@csun.edu
- Received by editor(s): March 22, 2017
- Published electronically: October 23, 2017
- Additional Notes: The first author was partially supported by NSF FRG grants DMS-1265290 and DMS-1463733, and by NSA grant H98230-14-1-0145. The second author was partially supported by NSF FRG grant DMS-1265290 and NSF grant DMS-1602054. The third author was partially supported by NSA grant 131011 and NSF grant DMS-15-02227.
- © Copyright 2017 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 55 (2018), 239-287
- MSC (2010): Primary 11-02, 14-02, 11G20, 12F12, 14G17, 14H30, 14H37, 14J50
- DOI: https://doi.org/10.1090/bull/1594
- MathSciNet review: 3777018
Dedicated: Dedicated to Yvonne Abhyankar