FRENCH

Hyperrésolutions cubiques et descente cohomologique

By F. Guillén , V. Navarro Aznar , P. Pascual-Gainza , F. Puerta (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1988
ISBN
9780387500232, 0-387-50023-5
DOI
10.1007/BFb0085054
LCC
QA3 .L28 no. 1335,QA564 .L28 no. 1335
Open Library ID
OL2043213M
Language
french
Format
DJVU
Filesize
1018 kB (1042255 bytes)
Series
Lecture Notes in Mathematics 1335
Edition
1
Pages
192\206
Topic
Mathematics Algebra
Library
mexmat
Time added
2009-07-20 03:45:11
Algebraic Geometry

Description

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.

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