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  • © 1988

Hyperresolutions cubiques et descente cohomologique

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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
  2. Hyperresolutions cubiques

    • F. Guillen
    Pages 1-42
  3. Theoremes sur la monodromie

    • P. Pascual Gainza
    Pages 43-58
  4. Theoremes d'annulation

    • 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: 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

Buying options

eBook USD 19.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 26.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions