On considère le groupe de cohomologie d’un espace compact localement hermitien symétrique à coefficients dans le faisceau des germes de sections holomorphes d’un tel espace fibré holomorphe sur l’espace qui est défini par un facteur d’automorphie. On rappelle d’abord brièvement des résultats classiques sur ce groupe de cohomologie, et on discute des théorèmes d’annulation sur le groupe de cohomologie.
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.
@article{AIF_1987__37_4_225_0,
author = {Murakami, Shingo},
title = {Vanishing theorems on cohomology associated to hermitian symmetric spaces},
journal = {Annales de l'Institut Fourier},
volume = {37},
year = {1987},
pages = {225-233},
doi = {10.5802/aif.1119},
mrnumber = {89j:32043},
zbl = {0625.57023},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1987__37_4_225_0}
}
Murakami, Shingo. Vanishing theorems on cohomology associated to hermitian symmetric spaces. Annales de l'Institut Fourier, Tome 37 (1987) pp. 225-233. doi : 10.5802/aif.1119. http://gdmltest.u-ga.fr/item/AIF_1987__37_4_225_0/
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