By Pedro Pascual-Gainza, Fernando Puerta

This monograph establishes a basic context for the cohomological use of Hironaka's theorem at the answer of singularities. It provides the speculation of cubical hyperresolutions, and this yields the cohomological houses of common algebraic kinds, following Grothendieck's normal rules on descent as formulated by way of Deligne in his procedure for simplicial cohomological descent. those hyperrésolutions are utilized in difficulties relating most likely singular kinds: the monodromy of a holomorphic functionality outlined on a posh analytic house, the De Rham cohmomology of types over a box of 0 attribute, Hodge-Deligne thought and the generalization of Kodaira-Akizuki-Nakano's vanishing theorem to singular algebraic types. As a edition of a similar principles, an software of cubical quasi-projective hyperresolutions to algebraic K-theory is given.

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