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Faisceaux pervers des cycles \'evanescents des vari\'et\'es de Drinfeld et groupes de cohomologie du mod\`ele de Deligne-Carayol

Pascal Boyer
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Abstract

In the first half of the paper, we translate in the geometric situation of Drinfeld varieties, the principal results of the Harris and Taylor's book. We give in particular the restriction to the open strata of the vanishing cycles sheaves in terms of some local systems named Harris-Taylor's local systems which we calculate the alternated sum of the cohomology group with compact supports. In the last half of the paper, we describe the monodromy filtration of the vanishing cycles perverse sheaf and the spectral sequence associated to it. Thanks to the Berkovich-Fargues' theorem, we obtain the description of the local monodromy filtration of the Deligne-Carayol model.

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Pascal Boyer. 2006-02-06. Faisceaux pervers des cycles \'evanescents des vari\'et\'es de Drinfeld et groupes de cohomologie du mod\`ele de Deligne-Carayol. https://arxiv.org/abs/math/0602096

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