Lecture Notes in Mathematics

Hyperresolutions cubiques et descente cohomologique

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

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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 hyperr├ęsolutions 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.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Hyperresolutions cubiques

    Pages 1-42

    Guillen, F.

  • Theoremes sur la monodromie

    Pages 43-58

    Gainza, P. Pascual

  • Descente cubique de la cohomologie de De Rham algebrique

    Pages 59-86

    Guillen, F.

  • Applications des hyperresolutions cubiques a la theorie de hodge

    Pages 87-132

    Puerta, F.

  • Theoremes d'annulation

    Pages 133-160

    Aznar, V. Navarro

Buy this book

eBook $19.99
price for USA in USD
  • ISBN 978-3-540-69984-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $26.00
price for USA in USD
  • ISBN 978-3-540-50023-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Hyperresolutions cubiques et descente cohomologique
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1335
Copyright
1988
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69984-2
DOI
10.1007/BFb0085054
Softcover ISBN
978-3-540-50023-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 192
Topics