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
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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.

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Shreeram S. Abhyankar
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

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