Analytic cohomology of complete intersections in a Banach space
[Cohomologie d'une intersection complète dans un espace de Banach]
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 147-158.

Let X be a Banach space with a countable unconditional basis (e.g., X=2), ΩX an open set and f1,...,fk complex-valued holomorphic functions on Ω, such that the Fréchet differentials df1(x),...,dfk(x) are linearly independant over at each xΩ. We suppose that M={xΩ:f1(x)=...=fk(x)=0} is a complete intersection and we consider a holomorphic Banach vector bundle EM. If I (resp.𝒪E) denote the ideal of germs of holomorphic functions on Ω that vanish on M (resp. the sheaf of germs of holomorphic sections of E), then the sheaf cohomology groups Hq(Ω,I), Hq(M,𝒪E) vanish for all q1.

On démontre par exemple que dans un espace de Hilbert séparable au-dessus d’une intersection complète lisse M tous les fibrés vectoriels holomorphes sont acycliques, et le faisceau idéal de M est au-dessus des voisinages pseudoconvexes ouverts de M assez petit.

DOI : 10.5802/aif.2013
Classification : 32L20, 32L10, 46G20
Keywords: analytic cohomology, complete intersections
Mots-clés : cohomologie analytique, intersection complète

Patyi, Imre 1

1 University of California at Riverside, Department of Mathematics, Riverside CA 92521-0135 (USA)
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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. https://numdam.org/articles/10.5802/aif.2013/

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