Download Local Homotopy Theory (Springer Monographs in Mathematics) by John F. Jardine PDF

By John F. Jardine

This monograph at the homotopy conception of topologized diagrams of areas and spectra supplies knowledgeable account of a topic on the beginning of motivic homotopy idea and the idea of topological modular varieties in good homotopy theory.

Beginning with an creation to the homotopy conception of simplicial units and topos thought, the publication covers center issues similar to the risky homotopy concept of simplicial presheaves and sheaves, localized theories, cocycles, descent concept, non-abelian cohomology, stacks, and native sturdy homotopy thought. an in depth remedy of the formalism of the topic is interwoven with causes of the inducement, improvement, and nuances of rules and effects. The coherence of the summary idea is elucidated by using broadly acceptable instruments, reminiscent of Barr's theorem on Boolean localization, version constructions at the classification of simplicial presheaves on a website, and cocycle different types. A wealth of concrete examples exhibit the energy and value of the topic in topology, quantity concept, algebraic geometry, and algebraic K-theory.

Assuming easy wisdom of algebraic geometry and homotopy thought, Local Homotopy Theory will entice researchers and complicated graduate scholars trying to comprehend and improve the purposes of homotopy thought in a number of components of arithmetic and the mathematical sciences.

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