Projective polynomials
HTML articles powered by AMS MathViewer
- by Shreeram S. Abhyankar PDF
- Proc. Amer. Math. Soc. 125 (1997), 1643-1650 Request permission
Abstract:
Certain nice trinomials have the projective linear groups as their Galois groups. This was proved using considerable group theory. Here is an easier proof based on the observation that the said trinomials are what may be called projective polynomials. It extends the results to a local situation.References
- Shreeram Abhyankar, Coverings of algebraic curves, Amer. J. Math. 79 (1957), 825–856. MR 94354, DOI 10.2307/2372438
- Shreeram S. Abhyankar, Galois theory on the line in nonzero characteristic, Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 1, 68–133. MR 1118002, DOI 10.1090/S0273-0979-1992-00270-7
- Shreeram S. Abhyankar, Nice equations for nice groups, Israel J. Math. 88 (1994), no. 1-3, 1–23. MR 1303488, DOI 10.1007/BF02937504
- S. S. Abhyankar, Fundamental group of the affine line in positive characteristic, Proceedings of the 1992 International Colloquium on Geometry and Analysis, Tata Institute of Fundamental Research, Bombay (1995), 1-26.
- S. S. Abhyankar, Mathieu group coverings and linear group coverings, Contemporary Mathematics 186 (1995), 293-319.
- S. S. Abhyankar, Again nice equations for nice groups, Proceedings of the American Mathematical Society, (To Appear).
- S. S. Abhyankar, More nice equations for nice groups, Proceedings of the American Mathematical Society, (To Appear).
- S. S. Abhyankar, Further nice equations for nice groups, Transactions of the American Mathematical Society, (To Appear).
- S. S. Abhyankar, Local fundamental groups of algebraic varieties, pp. (To Appear).
- P. J. Cameron and W. M. Kantor, $2$-transitive and antiflag transitive collineation groups of finite projective spaces, J. Algebra 60 (1979), no. 2, 384–422. MR 549937, DOI 10.1016/0021-8693(79)90090-5
- Cahit Arf, Untersuchungen über reinverzweigte Erweiterungen diskret bewerteter perfekter Körper, J. Reine Angew. Math. 181 (1939), 1–44 (German). MR 18, DOI 10.1515/crll.1940.181.1
Additional Information
- Shreeram S. Abhyankar
- Email: ram@cs.purdue.edu
- Received by editor(s): January 5, 1996
- Additional Notes: This work was partly supported by NSF grant DMS 91–01424 and NSA grant MDA 904–92–H–3035.
- Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1643-1650
- MSC (1991): Primary 12F10, 14H30, 20D06, 20E22
- DOI: https://doi.org/10.1090/S0002-9939-97-03939-7
- MathSciNet review: 1403111
Dedicated: Dedicated to J-P. Serre for his Seventieth Birthday