Congruences between Siegel modular forms on the level of group cohomology
Annales de l'Institut Fourier, Volume 46 (1996) no. 4, p. 877-897

Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of GSp(4), giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible classes of parabolic subgroups.

Les formes modulaires de Siegel à valeurs vectorielles se trouvent dans certains groupes de cohomologie dont les coefficients sont des représentations irréductibles de groupes symplectiques. En utilisant la fonctorialité par rapport aux coefficients, on montre que les composantes ordinaires de la cohomologie ne dépendent pas du poids. Le sens de ordinaire dépend d’un choix de sous-groupe parabolique de GSp(4), ce qui donne une certaine direction au changement de poids. Nos résultats complètent ceux de Taylor et Tilouine-Urban pour les autres classes de sous-groupes paraboliques.

@article{AIF_1996__46_4_877_0,
     author = {Buecker, Karsten},
     title = {Congruences between Siegel modular forms on the level of group cohomology},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {4},
     year = {1996},
     pages = {877-897},
     doi = {10.5802/aif.1533},
     zbl = {0853.11038},
     mrnumber = {98f:11038},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1996__46_4_877_0}
}
Buecker, Karsten. Congruences between Siegel modular forms on the level of group cohomology. Annales de l'Institut Fourier, Volume 46 (1996) no. 4, pp. 877-897. doi : 10.5802/aif.1533. http://www.numdam.org/item/AIF_1996__46_4_877_0/

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