Sur l'indépendance l-adique de nombres algébriques |
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Authors: | Jean-François Jaulent |
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Institution: | Université de Franche-Comté, Faculté des Sciences, Mathématiques, F25030 Besancon Cedex, France |
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Abstract: | Let l a prime number and K a Galois extension over the field of rational numbers, with Galois group G. A conjecture is put forward on l-adic independence of algebraic numbers, which generalizes the classical ones of Leopoldt and Gross, and asserts that the l-adic rank of a G submodule of Kx depends only on the character of its Galois representation. When G is abelian and in some other cases, a proof is given of this conjecture by using l-adic transcendence results. |
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