Abstract
In 1960, H. Grauert proved the following coherence theorem [2]: Let X, Y be complex spaces and π: X → Y a proper holomorphic map. Then, for every coherent analytic sheaf J on X, all direct image sheaves Rnπ*J are coherent. We give a new proof of this theorem, based on ideas of B. Malgrange. This proof does not use induction on the dimension of the base space Y and can be generalized to relative-analytic spaces X → Y where Y belongs to a bigger category of ringed spaces, which contains in particular all complex spaces and differentiable manifolds.
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