Abhyankar, Shreeram S. ; Sundaram, Ganapathy S.
(1997)
*Galois theory of Moore-Carlitz-Drinfeld modules
*
Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, 325
(4).
pp. 349-353.
ISSN 0764-4442

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/S0764-4442(97)85615-7

## Abstract

In 1896, E. H. Moore showed that the Galois group of the generic vectorial (= additive) q-polynomial of q-degree m is GL(m,q), where m > 0 is any integer and q > 1 is any power of any prime p. We show that, for any integer n > 0, the Galois group of the n-th iterate of the said polynomial is the generalized general linear group GL(m, q, n) consisting of all m by m matrices with invertible determinant over the local ring GF(q)[T]/T^{n}. For m=1, this was proved by Carlitz in 1938 as part of his explicit class field theory over finite fields. The case of m=1 was further enhanced by Drinfeld in 1974.

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ID Code: | 70885 |

Deposited On: | 22 Nov 2011 12:57 |

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