Hyperresolutions Cubiques et Descente Cohomologique - Francisco Guillen - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783540500230 - July 27, 1988
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Francisco Guillen
Hyperresolutions Cubiques et Descente Cohomologique French, 1988 edition

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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 hyperrésolutions 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.

212 pages, black & white illustrations

Media Books     Paperback Book   (Book with soft cover and glued back)
Released July 27, 1988
ISBN13 9783540500230
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 212
Dimensions 156 × 234 × 11 mm   ·   303 g
Language French  

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