P-adic local Langlands correspondence and geometry

Abstract : This thesis concerns the geometry behind the p-adic local Langlands correspondence. We give a formalism of methods of Emerton, which would permit to establish the Fontaine-Mazur conjecture in the general case for unitary groups. Then, we verify that our formalism works well in the case of U(3) where we use the construction of Breuil-Herzig as the input for the p-adic correspondence.From the local viewpoint, we start a study of the modulo p and p-adic cohomology of the Lubin-Tate tower for GL_2(Q_p). In particular, we show that we can find the local p-adic Langlands correspondence in the completed cohomology of the Lubin-Tate tower.
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Przemyslaw Chojecki. P-adic local Langlands correspondence and geometry. Number Theory [math.NT]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066035⟩. ⟨tel-01178288⟩

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