Sur une conjecture de Kottwitz au bord  [ On a conjecture of Kottwitz at the boundary ]
Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 45 (2012) no. 1, p. 143-165
We are interested in the intersection cohomology of the minimal compactification of Siegel modular varieties at some places of bad reduction. We compute the semi-simple trace of the Frobenius morphism on the fibers of the nearby cycles of the intersection complex. We obtain a common generalization of results of Morel, Haines and Ngô.
Nous nous intéressons à la cohomologie d'intersection de la compactification minimale des variétés de Siegel à certaines places de mauvaise réduction. Nous calculons la trace semi-simple du morphisme de Frobenius sur les fibres des cycles proches du complexe d'intersection. Nous obtenons une généralisation commune de résultats de Morel et de Haines et Ngô.
DOI : https://doi.org/10.24033/asens.2162
Classification:  14F20,  14K10
Keywords: Shimura variety, Siegel variety, bad reduction, semi-simple L function, intersection complex
@article{ASENS_2012_4_45_1_143_0,
     author = {Stroh, Beno\^\i t},
     title = {Sur une conjecture de Kottwitz au bord},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {4e s{\'e}rie, 45},
     number = {1},
     year = {2012},
     pages = {143-165},
     doi = {10.24033/asens.2162},
     mrnumber = {2961789},
     language = {fr},
     url = {http://www.numdam.org/item/ASENS_2012_4_45_1_143_0}
}
Stroh, Benoît. Sur une conjecture de Kottwitz au bord. Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 45 (2012) no. 1, pp. 143-165. doi : 10.24033/asens.2162. http://www.numdam.org/item/ASENS_2012_4_45_1_143_0/

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