[Cohomology with compact support of a space over the Bruhat-Tits building of over a local field. Cuspidal representations of level zero.]
Let the group , where is a non-archimedean locally compact field, and its Bruhat-Tits building. We construct a simplicial complex , equipped with an action of and with a -equivariant proper simplicial projection . We prove that the cohomology with compact support in higher dimensions contains as subquotients all irreducible cuspidal level zero representations.
Soit le groupe , où est un corps localement compact non-archimédien, et son immeuble de Bruhat-Tits. Nous construisons un complexe simplicial , doté d’une action de et d’une projection propre simpliciale -équivariante . Nous démontrons qu’en dimension supérieure la cohomologie à support compact contient comme sous-quotient toutes les représentations cuspidales irréductibles de niveau zéro.
Revised:
Accepted:
Published online:
DOI: 10.5802/cml.47
Keywords: Representations of the general linear $p$-adic groups, Bruhat-Tits buildings, Cohomology with compact support.
@article{CML_2018__10_1_95_0, author = {Rajhi, Anis}, title = {Cohomologie \`a support compact d{\textquoteright}un espace au-dessus de l{\textquoteright}immeuble de {Bruhat-Tits} de ${\protect \rm GL}_{n}$ sur un corps local. {Repr\'esentations} cuspidales de niveau z\'ero.}, journal = {Confluentes Mathematici}, pages = {95--124}, publisher = {Institut Camille Jordan}, volume = {10}, number = {1}, year = {2018}, doi = {10.5802/cml.47}, mrnumber = {3869012}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/cml.47/} }
TY - JOUR AU - Rajhi, Anis TI - Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de ${\protect \rm GL}_{n}$ sur un corps local. Représentations cuspidales de niveau zéro. JO - Confluentes Mathematici PY - 2018 SP - 95 EP - 124 VL - 10 IS - 1 PB - Institut Camille Jordan UR - http://www.numdam.org/articles/10.5802/cml.47/ DO - 10.5802/cml.47 LA - fr ID - CML_2018__10_1_95_0 ER -
%0 Journal Article %A Rajhi, Anis %T Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de ${\protect \rm GL}_{n}$ sur un corps local. Représentations cuspidales de niveau zéro. %J Confluentes Mathematici %D 2018 %P 95-124 %V 10 %N 1 %I Institut Camille Jordan %U http://www.numdam.org/articles/10.5802/cml.47/ %R 10.5802/cml.47 %G fr %F CML_2018__10_1_95_0
Rajhi, Anis. Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de ${\protect \rm GL}_{n}$ sur un corps local. Représentations cuspidales de niveau zéro.. Confluentes Mathematici, Volume 10 (2018) no. 1, pp. 95-124. doi : 10.5802/cml.47. http://www.numdam.org/articles/10.5802/cml.47/
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