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Analytic cohomology of complete intersections in a Banach space

Imre Patyi — 2004

Annales de l’institut Fourier

Let X be a Banach space with a countable unconditional basis (e.g., X = 2 ), Ω X an open set and f 1 , ... , f k complex-valued holomorphic functions on Ω , such that the Fréchet differentials d f 1 ( x ) , ... , d f k ( x ) are linearly independant over 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...

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