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.
Read Online or Download Hyperrésolutions cubiques et descente cohomologique PDF
Similar Algebraic Geometry books
The Iranian revolution nonetheless baffles such a lot Western observers. Few thought of the increase of theocracy in a modernized kingdom attainable, and less notion it could outcome from a well-liked revolution. stated Amir Arjomand's The Turban for the Crown presents a considerate, painstakingly researched, and intelligible account of the turmoil in Iran which finds the significance of this singular occasion for our realizing of revolutions.
First textbook-level account of uncomplicated examples and methods during this zone. appropriate for self-study through a reader who understands a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.
This ebook introduces the speculation of modular kinds, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner idea; Hecke eigenforms and their mathematics houses; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms.
In keeping with a path given to gifted high-school scholars at Ohio collage in 1988, this booklet is largely a complicated undergraduate textbook concerning the arithmetic of fractal geometry. It properly bridges the space among conventional books on topology/analysis and extra really good treatises on fractal geometry.
Extra info for Hyperrésolutions cubiques et descente cohomologique