F. Guillén, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta (auth.)9780387500232, 0-387-50023-5
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. |
Table of contents :
Hyperresolutions cubiques….Pages 1-42
Theoremes sur la monodromie….Pages 43-58
Descente cubique de la cohomologie de De Rham algebrique….Pages 59-86
Applications des hyperresolutions cubiques a la theorie de hodge….Pages 87-132
Theoremes d’annulation….Pages 133-160
Descente cubique pour la K-theorie des faisceaux coherents et l’homologie de Chow….Pages 161-188 |
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