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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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Keywords: Dolbeault cohomology, sheaf cohomology, Stein manifold, linear topological space, differential form
Article copyright: © Copyright 1975 American Mathematical Society