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Hyperresolutions cubiques et descente cohomologique

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  • © 1988

Overview

Authors:
  1. F. Guillén
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  2. V. Navarro Aznar
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  3. P. Pascual-Gainza
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  4. F. Puerta
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1335)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XII
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  2. Hyperresolutions cubiques

    • F. Guillen
    Pages 1-42

  3. Theoremes sur la monodromie

    • P. Pascual Gainza
    Pages 43-58

  4. Descente cubique de la cohomologie de De Rham algebrique

    • F. Guillen
    Pages 59-86

  5. Applications des hyperresolutions cubiques a la theorie de hodge

    • F. Puerta
    Pages 87-132

  6. Theoremes d'annulation

    • V. Navarro Aznar
    Pages 133-160

  7. Descente cubique pour la K-theorie des faisceaux coherents et l'homologie de Chow

    • P. Pascual Gainza
    Pages 161-188

  8. Back Matter

    Pages 189-194
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About this book

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.

Bibliographic Information

  • Book Title: Hyperresolutions cubiques et descente cohomologique

  • Authors: F. Guillén, V. Navarro Aznar, P. Pascual-Gainza, F. Puerta

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0085054

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-50023-0Published: 27 July 1988

  • eBook ISBN: 978-3-540-69984-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 192

  • Topics: Algebraic Geometry

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