Titlebook: Local Homotopy Theory; John F. Jardine Book 2015 Springer-Verlag New York 2015 algebraic K-theory.higher category theory.homotopical algeb

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Local Homotopy Theory978-1-4939-2300-7Series ISSN 1439-7382 Series E-ISSN 2196-9922

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John F. JardineEquips the reader with the background necessary to understand recent advances in homotopy theory and algebraic geometry.Written by one of the main contributors to the field.Goes beyond the formalism o

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https://doi.org/10.1007/978-1-4939-2300-7algebraic K-theory; higher category theory; homotopical algebra; homotopy theory; model categories; motiv

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Local Model Structuress is also displayed..Injective fibrant models and homotopy theoretic descent theory are introduced. The calculational utility of descent theory is discussed, and the major geometric descent theorems, for the Zariski and Nisnevich topologies on a regular scheme, are proved.

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Homology Sheaves and Cohomology Groupsr presheaves of chain complexes on the Nisnevich site of a scheme. The localization technique can be extended to additive contravariant functors to chain complexes which are defined on categories with objects in a site which are enriched in abelian groups. Sample outcomes include Voevodsky‘s category of effective motives on a perfect field.

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1439-7382 e main contributors to the field.Goes beyond the formalism o.This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory..Be

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Cocycleslocal homotopy theory: it is used in later chapters to establish homotopy classification results for abelian and non-abelian sheaf cohomology theories, and to establish a theory of cup products. The theory of cocycles also leads to a fast proof of a widely applicable version of the Verdier hypercovering theorem.