© 1988

Hyperrésolutions cubiques et descente cohomologique

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1335)

Table of contents

  1. Front Matter
    Pages I-XII
  2. F. Guillen
    Pages 1-42
  3. P. Pascual Gainza
    Pages 43-58
  4. V. Navarro Aznar
    Pages 133-160
  5. Back Matter
    Pages 189-194

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 Hyperrésolutions cubiques et descente cohomologique
  • Authors Francisco Guillen
    Vincente Navarro Aznar
    Pedro Pascual-Gainza
    Fernando Puerta
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-50023-0
  • eBook ISBN 978-3-540-69984-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XII, 192
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site
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