# Le morphisme déterminant pour les espaces de modules de groupes p-divisibles

Abstract : Let \M be a moduli space of p-divisible groups introduced by Rapoport and Zink. Assume that \M is unramified of EL or PEL type which is unitary or symplectic. Let \Mrig be the generic fiber of Berthelot of \M. This is a rigid analytic space over which there exist a tower of finite etale coverings (\M_K)_K classifing the level structures. We define a determinant morphism \det_K from the tower (\M_K)_K to a tower of rigid analytic spaces of dimension 0 associated to the cocenter of the reductive group related to the space \M. This is a local analogue on the nonarchimedean places of the determinant morphism for Shimura varieties defined by Deligne. As for Shimura varieties, we prove that the geometric fibers of the determinant morphism \det_K are the geometrically connected components of \M_K. We define also the exterior power morphisms which generalize the determinant morphism on the tower of rigid analytic spaces associated to a Lubin-Tate space.
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Miaofen Chen. Le morphisme déterminant pour les espaces de modules de groupes p-divisibles. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112058⟩. ⟨tel-00594110⟩

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