On démontre par exemple que dans un espace de Hilbert séparable au-dessus d’une intersection complète lisse tous les fibrés vectoriels holomorphes sont acycliques, et le faisceau idéal de est au-dessus des voisinages pseudoconvexes ouverts de assez petit.
Let be a Banach space with a countable unconditional basis (e.g., ), an open set and complex-valued holomorphic functions on , such that the Fréchet differentials are linearly independant over at each . We suppose that is a complete intersection and we consider a holomorphic Banach vector bundle . If (resp.) denote the ideal of germs of holomorphic functions on that vanish on (resp. the sheaf of germs of holomorphic sections of ), then the sheaf cohomology groups , vanish for all .
Classification : 32L20, 32L10, 46G20
Mots clés : cohomologie analytique, intersection complète
@article{AIF_2004__54_1_147_0, author = {Patyi, Imre}, title = {Analytic cohomology of complete intersections in a Banach space}, journal = {Annales de l'Institut Fourier}, pages = {147--158}, publisher = {Association des Annales de l'institut Fourier}, volume = {54}, number = {1}, year = {2004}, doi = {10.5802/aif.2013}, zbl = {1080.32017}, language = {en}, url = {archive.numdam.org/item/AIF_2004__54_1_147_0/} }
Patyi, Imre. Analytic cohomology of complete intersections in a Banach space. Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 147-158. doi : 10.5802/aif.2013. http://archive.numdam.org/item/AIF_2004__54_1_147_0/
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