Projective polynomials
Author:
Shreeram S. Abhyankar
Journal:
Proc. Amer. Math. Soc. 125 (1997), 16431650
MSC (1991):
Primary 12F10, 14H30, 20D06, 20E22
MathSciNet review:
1403111
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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.
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 [1]
 S. S. Abhyankar, Coverings of algebraic curves, Amer. J. Math. 79 (1957), 825856. MR 20:872
 [2]
 S. S. Abhyankar, Galois theory on the line in nonzero characteristic, Bull. A.M.S. 27 (1992), 68133. MR 94a:12004
 [3]
 S. S. Abhyankar, Nice equations for nice groups, Israel J. Math. 88 (1994), 124. MR 96f:12003
 [4]
 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), 126. CMP 96:01
 [5]
 S. S. Abhyankar, Mathieu group coverings and linear group coverings, Contemporary Mathematics 186 (1995), 293319. CMP 96:01
 [6]
 S. S. Abhyankar, Again nice equations for nice groups, Proceedings of the American Mathematical Society, (To Appear). CMP 95:16
 [7]
 S. S. Abhyankar, More nice equations for nice groups, Proceedings of the American Mathematical Society, (To Appear). CMP 95:16
 [8]
 S. S. Abhyankar, Further nice equations for nice groups, Transactions of the American Mathematical Society, (To Appear). CMP 96:09
 [9]
 S. S. Abhyankar, Local fundamental groups of algebraic varieties, pp. (To Appear). CMP 95:16
 [10]
 P. J. Cameron and W. M. Kantor, 2Transitive and antiflag transitive collineation groups of finite projective spaces, J. of Algebra 60 (1979), 384422. MR 81c:20032
 [11]
 L. Carlitz, Resolvents of certain linear groups in a finite field, Canad. J. Math. 8 (1956), 568579. MR 18:377f
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Additional Information
Shreeram S. Abhyankar
Email:
ram@cs.purdue.edu
DOI:
http://dx.doi.org/10.1090/S0002993997039397
PII:
S 00029939(97)039397
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.
Dedicated:
Dedicated to JP. Serre for his Seventieth Birthday
Communicated by:
Ronald M. Solomon
Article copyright:
© Copyright 1997 American Mathematical Society
