Représentations de Weil pour les groupes de similitudes et changement de base

Abstract : This present thesis is working on the Weil representation. It consists of three parts. In chapter 2 and chapter 3, we generalize the Howe correspondance for the similitudes groupes over the non archimedien field with odd residual characteristic. In chapter 4 and chapter 5, we answer one question, raised by V. Drinfeld, about the restriction of the Weil representation of the group GSp8(F) to GL2(A) where A is an étale algebra over a non archimedien field or a finite field F. On the other hand, in the chapter 5, we prove that in finite field case, the Weil representations are invariant under the operator of base change in the sens of Shintani-lifting.
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Chun Hui Wang. Représentations de Weil pour les groupes de similitudes et changement de base. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2012. Français. ⟨NNT : 2012PA112110⟩. ⟨tel-00759639⟩

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