Hyperresolutions cubiques et descente cohomologique

di Francisco Guillen (Autore)

Vincente Navarro Aznar (Autore)

Pedro Pascual-Gainza (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1988

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.

• Autore: Francisco Guillen, Vincente Navarro Aznar, Pedro Pascual-Gainza
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Lecture Notes in Mathematics
• Anno: 1988
• Rilegatura: Paperback / softback
• Pagine: 192 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783540500230

Testo in French