no. 1
Analytic cohomology of complete intersections in a Banach space
[Cohomologie d'une intersection complète dans un espace de Banach]
Patyi, Imre1
1 University of California at Riverside, Department of Mathematics, Riverside CA 92521-0135 (USA)
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 147-158.

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.

Let X be a Banach space with a countable unconditional basis (e.g., X=ℓ 2 ), Ω⊂X an open set and f 1 ,...,f k complex-valued holomorphic functions on Ω, such that the Fréchet differentials df 1 (x),...,df k (x) are linearly independant over ℂ at each x∈Ω. We suppose that M={x∈Ω:f 1 (x)=...=f k (x)=0} is a complete intersection and we consider a holomorphic Banach vector bundle E→M. If I (resp.𝒪 E ) 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 H q (Ω,I), H q (M,𝒪 E ) vanish for all q≥1.

DOI : 10.5802/aif.2013
Classification : 32L20, 32L10, 46G20
Keywords: analytic cohomology, complete intersections
Mot 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. http://www.numdam.org/articles/10.5802/aif.2013/

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