Hyperrésolutions cubiques et descente cohomologique / by F. Guillén, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta.

Format:

Book

Author/Creator:

Guillén, F., 1956- author.

Aznar, V. Navarro, author.

Pascual-Gainza, P., author.

Puerta, F., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1335.

Lecture Notes in Mathematics, 0075-8434 ; 1335

Language:

French

Subjects (All):

Geometry, Algebraic.

Algebraic Geometry.

Local Subjects:

Algebraic Geometry.

Physical Description:

1 online resource (XII, 192 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540699842

Access Restriction:

Restricted for use by site license.