Hyperrésolutions cubiques et descente cohomologique / F. Guillén [and others].

Contributor(s): Guillén, F, 1956-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1335.Publisher: Berlin ; New York : Springer-Verlag, ©1988Description: 1 online resource (xii, 192 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540699842; 3540699848Subject(s): Algebraic varieties | Homology theory | K-theory | Functions of complex variables | Hodge, Théorie de | Homologie | Variétés algébriques | Algebraic varieties | Functions of complex variables | Homology theory | K-theory | Algebraische Mannigfaltigkeit | Auflösung von SingularitätenGenre/Form: Electronic books. Additional physical formats: Print version:: Hyperrésolutions cubiques et descente cohomologique.DDC classification: 510.8 LOC classification: QA3 | .L28 no. 1335 | QA564Other classification: 31.51 Online resources: Click here to access online
Contents:
Table des matires: Hyperrsolutions cubiques -- Thormes sur la monodromie -- Descente cubique de la cohomologie de De Rham algbrique -- Applications des hyperrsolutions cubiques la thorie de Hodge -- Thormes d'annulation -- Descente cubique pour la K-thorie des faisceaux cohrents et l'homologie de Chow -- Index terminoloque.
Summary: This monograph establishes a general context for the cohomological use of Hironaka's theorem on the resolution of singularities. It presents the theory of cubical hyperresolutions, and this yields the cohomological properties of general algebraic varieties, following Grothendieck's general ideas on descent as formulated by Deligne in his method for simplicial cohomological descent. These hyperrsolutions are applied in problems concerning possibly singular varieties: the monodromy of a holomorphic function defined on a complex analytic space, the De Rham cohmomology of varieties over a field of zero characteristic, Hodge-Deligne theory and the generalization of Kodaira-Akizuki-Nakano's vanishing theorem to singular algebraic varieties. As a variation of the same ideas, an application of cubical quasi-projective hyperresolutions to algebraic K-theory is given.
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Includes bibliographical references and index.

Table des matires: Hyperrsolutions cubiques -- Thormes sur la monodromie -- Descente cubique de la cohomologie de De Rham algbrique -- Applications des hyperrsolutions cubiques la thorie de Hodge -- Thormes d'annulation -- Descente cubique pour la K-thorie des faisceaux cohrents et l'homologie de Chow -- Index terminoloque.

This monograph establishes a general context for the cohomological use of Hironaka's theorem on the resolution of singularities. It presents the theory of cubical hyperresolutions, and this yields the cohomological properties of general algebraic varieties, following Grothendieck's general ideas on descent as formulated by Deligne in his method for simplicial cohomological descent. These hyperrsolutions are applied in problems concerning possibly singular varieties: the monodromy of a holomorphic function defined on a complex analytic space, the De Rham cohmomology of varieties over a field of zero characteristic, Hodge-Deligne theory and the generalization of Kodaira-Akizuki-Nakano's vanishing theorem to singular algebraic varieties. As a variation of the same ideas, an application of cubical quasi-projective hyperresolutions to algebraic K-theory is given.

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