Hyperrésolutions cubiques et descente cohomologique
By: F. Guillén ... [et al.].
Contributors: Guillén, F., 1956-.
Series: Lecture notes in mathematics -- 1335.; Lecture notes in mathematics (Springer-Verlag) -- 1335.
Publisher: Springer-Verlag
Published: 1988
Place of publication: Berlin; New York
Language: fre
Number of pages: 192
Subjects: Hodge theory.; Homology theory.; Algebraic varieties.
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.
Notes: Includes bibliographies and index.