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AuthorGuillรฉn, F. author
TitleHyperrรฉsolutions cubiques et descente cohomologique [electronic resource] / by F. Guillรฉn, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1988
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Descript XII, 192 p. online resource


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 hyperrรฉsolutions 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


Hyperresolutions cubiques -- Theoremes sur la monodromie -- Descente cubique de la cohomologie de De Rham algebrique -- Applications des hyperresolutions cubiques a la theorie de hodge -- Theoremes d'annulation -- Descente cubique pour la K-theorie des faisceaux coherents et l'homologie de Chow

Mathematics Algebraic geometry Mathematics Algebraic Geometry


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