COHOMOLOGIE DES ESPACES DE LUBIN-TATE : UNE NOUVELLE PREUVE GÉOMÉTRIQUE NATURELLE

Abstract : In my paper at Inventiones 2009, we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle Ψ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf cohomology of both Harris-Taylor perverse sheaves and those of Ψ. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.
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Submitted on : Monday, November 7, 2016 - 3:43:28 PM
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Pascal Boyer. COHOMOLOGIE DES ESPACES DE LUBIN-TATE : UNE NOUVELLE PREUVE GÉOMÉTRIQUE NATURELLE. 2016. ⟨hal-01393513v1⟩

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