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Espaces de Rapoport-Zink et conjecture de Kottwitz

Abstract : The Kottwitz conjecture describes the cohomology of basic Rapoport-Zink spaces using local Langlands correspondences. At first, via geometrical studies of someKottwitz-type Shimura varieties, we prove this conjecture for basic simple unramifiedunitary PEL type Rapoport-Zink spaces of signature (1,n−1). In the second part,via the study of the modifications of vector bundles on the Fargues-Fontaine curve,we prove a geometric formula relating the Lubin-Tate towers with the simple basicunramified Rapoport-Zink spaces of EL type of signature (1,n−1), (p1; q1) ,....., (pk; qk) where piqi = 0. In particular, we deduce the computation of cohomology groups of the latter.
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Kieu Hieu Nguyen. Espaces de Rapoport-Zink et conjecture de Kottwitz. Théorie des nombres [math.NT]. Université Sorbonne Paris Cité, 2019. Français. ⟨NNT : 2019USPCD012⟩. ⟨tel-02905829⟩

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