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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 offers the speculation of cubical hyperresolutions, and this yields the cohomological homes of common algebraic forms, following Grothendieck's common principles on descent as formulated through Deligne in his technique for simplicial cohomological descent. those hyperrésolutions are utilized in difficulties relating in all likelihood singular kinds: the monodromy of a holomorphic functionality outlined on a fancy analytic house, the De Rham cohmomology of sorts over a box of 0 attribute, Hodge-Deligne idea and the generalization of Kodaira-Akizuki-Nakano's vanishing theorem to singular algebraic types. As a edition of an analogous principles, an program of cubical quasi-projective hyperresolutions to algebraic K-theory is given.

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