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

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