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Hyperrésolutions cubiques et descente cohomologique

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

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

Introduction

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

  • DOI https://doi.org/10.1007/BFb0085054
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50023-0
  • Online ISBN 978-3-540-69984-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site