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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the infinite dimensionality of the Dolbeault cohomology groups


Author: Henry B. Laufer
Journal: Proc. Amer. Math. Soc. 52 (1975), 293-296
MSC: Primary 32C35
DOI: https://doi.org/10.1090/S0002-9939-1975-0379887-2
MathSciNet review: 0379887
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Abstract: Let $ M$ be an open subset of a Stein manifold without isolated points. Let $ {\Omega ^p}$ be the sheaf of germs of holomorphic $ p$-forms on $ M$. Then $ {H^q}(M,{\Omega ^p})$ is either 0 or else infinite dimensional. $ {H^q}(M,\mathcal{S})$ may be nonzero and finite dimensional if $ M$ is the regular points of a Stein space or if $ \mathcal{S}$ is an arbitrary coherent sheaf over $ M$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0379887-2
Keywords: Dolbeault cohomology, sheaf cohomology, Stein manifold, linear topological space, differential form
Article copyright: © Copyright 1975 American Mathematical Society