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Local Homotopy Theory (Paperback, Softcover reprint of the original 1st ed. 2015)
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Local Homotopy Theory (Paperback, Softcover reprint of the original 1st ed. 2015)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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. Beginning with an
introduction to the homotopy theory of simplicial sets and topos
theory, the book covers core topics such as the unstable homotopy
theory of simplicial presheaves and sheaves, localized theories,
cocycles, descent theory, non-abelian cohomology, stacks, and local
stable homotopy theory. A detailed treatment of the formalism of
the subject is interwoven with explanations of the motivation,
development, and nuances of ideas and results. The coherence of the
abstract theory is elucidated through the use of widely applicable
tools, such as Barr's theorem on Boolean localization, model
structures on the category of simplicial presheaves on a site, and
cocycle categories. A wealth of concrete examples convey the
vitality and importance of the subject in topology, number theory,
algebraic geometry, and algebraic K-theory. Assuming basic
knowledge of algebraic geometry and homotopy theory, Local Homotopy
Theory will appeal to researchers and advanced graduate students
seeking to understand and advance the applications of homotopy
theory in multiple areas of mathematics and the mathematical
sciences.
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