Hyperrésolutions cubiques et descente cohomologique
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Bibliographic Information
Hyperrésolutions cubiques et descente cohomologique
（Lecture notes in mathematics, 1335）
Springer-Verlag, c1988
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Library & Science Information Center, Osaka Prefecture University
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Note
Authors: F. Guillén, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta
Includes bibliographical references and index
Description and Table of Contents
Description
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 hyperresolutions 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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