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 Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 2, Pages 262–287 (Mi izv1661)

On the homology theory of analytic sheaves

V. D. Golovin

Abstract: The homology groups of analytic sheaves constitute a natural tool in the theory of duality on complex spaces. In algebraic geometry, homology theory was worked out back in the fifties by Grothendieck. But the corresponding theory remained undeveloped in complex analytic geometry, although important work has been done in this direction by Ramis and Ruget, and by Andreotti and Kas. Homology sheaves and homology groups of analytic sheaves have been defined by the author in an earlier paper (Dokl. Akad. Nauk SSSR 225, № 1 (1975), 41–43). In the present paper, their basic properties are investigated. In particular, it is shown that there exist spectral sequences relating the homology groups to the $\operatorname{Ext}$ functors and the cohomology groups. For complex manifolds, a Poincare duality is obtained. It is also shown that there are spectral sequences relating the homology groups of analytic sheaves to the Aleksandrov-Chekh homology and the canonical homology defined by Sklyarenko.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:2, 239–260

Bibliographic databases:

UDC: 515.17
MSC: Primary 32C37; Secondary 32C35, 32C36

Citation: V. D. Golovin, “On the homology theory of analytic sheaves”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 262–287; Math. USSR-Izv., 16:2 (1981), 239–260

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Mohamed Kaddar, “Morphismes géométriquement plats et faisceaux dualisants”, Comptes Rendus Mathematique, 346:19-20 (2008), 1087
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