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Theses

Conjecture de Greenberg généralisée et capitulation dans les Zp-extensions d'un corps de nombres

Abstract : The subject of this thesis is Iwasawa theory. We take a particular interest in Greenberg's generalized
(multiple) conjecture (GG). After establishing a precise link whith several problems of capitulation for certain p-adic cohomology groups in degree 2, we propose a weakened version (GGf) of (GG). We
show that (GGf) is true under certain conditions, namely that the ground field F, contains a primitive p-th root of unity, a (p)-split imaginary quadratic field, and verifies Leopoldt's conjecture. The techniques of this work also allow us to retrieve and generalize
(especially in non-cyclotomic Zp-extensions) a number of classical results in Iwasawa theory.
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https://tel.archives-ouvertes.fr/tel-00012074
Contributor : David Vauclair <>
Submitted on : Monday, April 3, 2006 - 9:33:25 AM
Last modification on : Thursday, November 12, 2020 - 5:28:02 PM
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David Vauclair. Conjecture de Greenberg généralisée et capitulation dans les Zp-extensions d'un corps de nombres. Mathématiques [math]. Université de Franche-Comté, 2005. Français. ⟨tel-00012074⟩

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