Hyperrésolutions cubiques et descente cohomologique
Guillén, F.
Hyperrésolutions cubiques et descente cohomologique [electronic resource] / by F. Guillén, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta. - XII, 192 p. online resource. - Lecture Notes in Mathematics, 1335 0075-8434 ; . - Lecture Notes in Mathematics, 1335 .
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.
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.
9783540699842
10.1007/BFb0085054 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35
Hyperrésolutions cubiques et descente cohomologique [electronic resource] / by F. Guillén, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta. - XII, 192 p. online resource. - Lecture Notes in Mathematics, 1335 0075-8434 ; . - Lecture Notes in Mathematics, 1335 .
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.
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.
9783540699842
10.1007/BFb0085054 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35