Overview

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.

Full Product Details

Author:   Francisco Guillen ,  Vincente Navarro Aznar ,  Pedro Pascual-Gainza ,  Fernando Puerta
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1988 ed.
Volume:   1335
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.670kg
ISBN:  

9783540500230

ISBN 10:   3540500235
Pages:   192
Publication Date:   27 July 1988
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Language:   French

Table of 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.

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