A finiteness theorem for holomorphic Banach bundles
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 6 (2007) no. 1, p. 15-37
Let E be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form id +K where K is compact. Assume that the characteristic fiber of E has the compact approximation property. Let n be the complex dimension of X and 0qn. Then: If VX is a holomorphic vector bundle (of finite rank) with H q (X,V)=0, then dimH q (X,VE)<. In particular, if dimH q (X,𝒪)=0, then dimH q (X,E)<.
Classification:  32F10,  32C37
@article{ASNSP_2007_5_6_1_15_0,
     author = {Leiterer, J\"urgen},
     title = {A finiteness theorem for holomorphic Banach bundles},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {1},
     year = {2007},
     pages = {15-37},
     zbl = {1178.32016},
     mrnumber = {2341512},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2007_5_6_1_15_0}
}
Leiterer, Jürgen. A finiteness theorem for holomorphic Banach bundles. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 6 (2007) no. 1, pp. 15-37. http://www.numdam.org/item/ASNSP_2007_5_6_1_15_0/

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