By John F. Jardine
This monograph at the homotopy conception of topologized diagrams of areas and spectra supplies knowledgeable account of an issue on the beginning of motivic homotopy concept and the idea of topological modular varieties in reliable homotopy theory.
Beginning with an advent to the homotopy thought of simplicial units and topos idea, the publication covers middle themes akin to the risky homotopy concept of simplicial presheaves and sheaves, localized theories, cocycles, descent thought, non-abelian cohomology, stacks, and native strong homotopy conception. a close remedy of the formalism of the topic is interwoven with reasons of the inducement, improvement, and nuances of rules and effects. The coherence of the summary thought is elucidated by utilizing greatly appropriate instruments, similar to Barr's theorem on Boolean localization, version buildings at the class of simplicial presheaves on a domain, and cocycle different types. A wealth of concrete examples show the energy and significance of the topic in topology, quantity thought, algebraic geometry, and algebraic K-theory.
Assuming easy wisdom of algebraic geometry and homotopy conception, Local Homotopy Theory will entice researchers and complicated graduate scholars trying to comprehend and enhance the purposes of homotopy thought in a number of parts of arithmetic and the mathematical sciences.
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