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Algebraic Geometry

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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 solution of singularities. It offers the speculation of cubical hyperresolutions, and this yields the cohomological houses of common algebraic types, following Grothendieck's basic rules on descent as formulated through Deligne in his approach for simplicial cohomological descent. those hyperrésolutions are utilized in difficulties pertaining to almost certainly singular types: 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 conception and the generalization of Kodaira-Akizuki-Nakano's vanishing theorem to singular algebraic types. As a edition of an identical principles, an software of cubical quasi-projective hyperresolutions to algebraic K-theory is given.

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