# La cohomologie des espaces de Lubin-Tate est libre

Abstract : The principal result of this work is the freeness in the $\overline{\mathbb{Z}}_l$-cohomology of the Lubin-Tate tower. The strategy is of global nature and relies on studying the complexe of nearby cycles of some Shimura varieties of Kottwitz-Harris-Taylor types. We use the constructions on the filtrations of stratification of a free perverse sheaf and we prove that applied to the extension by zero of Harris-Taylor local systems as well to the perverse sheaf of nearby cycles, these constructions are \og !-saturated \fg, which means that all the cokernels of the adjunction morphisms $j_!j^* \rightarrow Id$ under consideration, are torsion-free.
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https://hal.archives-ouvertes.fr/hal-01492074
Contributor : Pascal Boyer <>
Submitted on : Friday, August 31, 2018 - 10:38:01 AM
Last modification on : Wednesday, February 6, 2019 - 1:25:47 AM
Document(s) archivé(s) le : Saturday, December 1, 2018 - 2:46:17 PM

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LT-libre-final.pdf
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• HAL Id : hal-01492074, version 2

### Citation

Pascal Boyer. La cohomologie des espaces de Lubin-Tate est libre. 2014. ⟨hal-01492074v2⟩

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