Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Semilinear transformations


Author: Shreeram S. Abhyankar
Journal: Proc. Amer. Math. Soc. 127 (1999), 2511-2525
MSC (1991): Primary 12F10, 14H30, 20D06, 20E22
Published electronically: May 4, 1999
MathSciNet review: 1676323
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In previous papers, nice trinomial equations were given for unramified coverings of the once punctured affine line in nonzero characteristic $p$ with the projective general group $\mathrm{PGL}(m,q)$ and the general linear group $\mathrm{GL}(m,q)$ as Galois groups where $m>1$ is any integer and $q>1$ is any power of $p$. These Galois groups were calculated over an algebraically closed ground field. Here we show that, when calculated over the prime field, as Galois groups we get the projective general semilinear group $\mathrm{P}\Gamma \mathrm{L}(m,q)$ and the general semilinear group $\Gamma \mathrm{L}(m,q)$. We also obtain the semilinear versions of the local coverings considered in previous papers.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 12F10, 14H30, 20D06, 20E22

Retrieve articles in all journals with MSC (1991): 12F10, 14H30, 20D06, 20E22


Additional Information

Shreeram S. Abhyankar
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ram@cs.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05400-3
PII: S 0002-9939(99)05400-3
Received by editor(s): March 5, 1997
Received by editor(s) in revised form: July 2, 1997
Published electronically: May 4, 1999
Additional Notes: This work was partly supported by NSF grant DMS 91-01424 and NSA grant MDA 904-97-1-0010
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society