La $\mathrm{Z}_l$-cohomologie du modèle de Deligne-Carayol est sans torsion

Details La $\mathrm{Z}_l$-cohomologie du modèle de Deligne-Carayol est sans torsion La $\mathrm{Z}_l$-cohomologie du modèle de Deligne-Carayol est sans torsion

2007-07-30

arxiv.org/abs/0707.4396v3

Mathematics

Algebraic Geometry

45 pages, 1 figures

Scientific paper

This article is the $\mathrm{Z}_l$-version of my paper "Monodromie du faisceau pervers des cycles \'evanescents de quelques vari\'et\'es de Shimura simples" in Invent. Math. 2009 vol 177 pp. 239-280, where we study the vanishing cycles of some unitary Shimura variety. The aim is to prove that the cohomology sheaves of this complexe are free so that, thanks to the main theorem of Berkovich on vanishing cycles, we can deduce that the $\mathrm{Z}_l$-cohomology of the model of Deligne-Carayol is free. There will be a second article which will be the $\mathrm{Z}_l$ version of my paper "Conjecture de monodromie-poids pour quelques vari\'t\'es de Shimura unitaires" in Compositio vol 146 part 2, pp. 367-403. The aim of this second article will be to study the torsion of the cohomology groups of these Shimura varieties.

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