Given a KHT Shimura variety with an action of its unramified Hecke algebra , we proved in [7], see also [12] for other PEL Shimura varieties, that its localized cohomology groups at a generic maximal ideal of , happen to be free. In this work, we obtain the same result for such that its associated Galois -representation is irreducible, under the hypothesis that , where is the reflex field, the dimension of the KHT Shimura variety and the residual characteristic.
Étant donnée une variété de Shimura unitaire de type KHT de dimension relative sur son corps reflex et munie de l’action de son algèbre de Hecke non ramifiée, nous prouvons dans [7], voir aussi [12] pour les autres variétés de Shimura de type PEL, que ses groupes de -cohomologie localisés en un idéal maximal générique de , sont libres. Dans ce travail, sous l’hypothèse que , nous montrons le même résultat pour tel que sa -représentation galoisienne associée, , est irréductible.
Accepted:
Published online:
Keywords: Shimura varieties, torsion in the cohomology, maximal ideal of the Hecke algebra, localized cohomology, Galois representation
Mot clés : Variétés de Shimura, torsion dans la cohomologie, algèbres de Hecke, localisation de la cohomologie, représentations galoisiennes
Pascal Boyer 1
@article{JEP_2023__10__199_0, author = {Pascal Boyer}, title = {Galois irreducibility implies cohomology~freeness for {KHT~Shimura~varieties}}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {199--232}, publisher = {\'Ecole polytechnique}, volume = {10}, year = {2023}, doi = {10.5802/jep.216}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.216/} }
TY - JOUR AU - Pascal Boyer TI - Galois irreducibility implies cohomology freeness for KHT Shimura varieties JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 199 EP - 232 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.216/ DO - 10.5802/jep.216 LA - en ID - JEP_2023__10__199_0 ER -
%0 Journal Article %A Pascal Boyer %T Galois irreducibility implies cohomology freeness for KHT Shimura varieties %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 199-232 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.216/ %R 10.5802/jep.216 %G en %F JEP_2023__10__199_0
Pascal Boyer. Galois irreducibility implies cohomology freeness for KHT Shimura varieties. Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 199-232. doi : 10.5802/jep.216. https://jep.centre-mersenne.org/articles/10.5802/jep.216/
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