Le théorème de Fermat-Goss

Denis, Laurent

doi:10.1090/S0002-9947-1994-1195509-1

Le théorème de Fermat-Goss
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by Laurent Denis PDF

Trans. Amer. Math. Soc. 343 (1994), 713-726 Request permission

Abstract:

The analogue of the Fermat equation and of the Fermat conjecture is studied by Goss [G], on the rational function fields in characteristic $p > 0$. We prove here that this equation has no nontrivial solutions. When $q = 2$, the method uses the canonical height on the t-module constructed in [D]. This method also gives finiteness theorems for some generalization of the Fermat equation in higher dimension.

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