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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Closedness of coboundary modules of analytic sheaves


Authors: Yum-tong Siu and Günther Trautmann
Journal: Trans. Amer. Math. Soc. 152 (1970), 649-658
MSC: Primary 32.50
DOI: https://doi.org/10.1090/S0002-9947-1970-0273068-9
MathSciNet review: 0273068
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Abstract: Suppose $ A$ is a subvariety of a complex space $ X$ and $ \mathcal{J}$ is a coherent analytic sheaf on $ X$. It is shown that, if the analytic sheaf $ \mathcal{H}_{A}^{\nu}(\mathcal{J})$ of local cohomology is coherent for $ 0 \leqq \nu \leqq q$, then for $ 0 \leqq \nu \leqq q$ the local cohomology group $ \mathcal{H}_{A}^{\nu}(X, \mathcal{J})$ with its natural topology is Hausdorff and hence is a Fréchet space.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0273068-9
Keywords: Coherent analytic sheaves, local cohomology, coboundary modules, Fréchet spaces
Article copyright: © Copyright 1970 American Mathematical Society