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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...
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