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[John F Jardine] Local Homotopy Theory (pdf){Zzzzz}[BЯ]

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Description

 							
  
  
  
  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.
  
  Product Description
  From the Back Cover
  
  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.
  About the Author
  
  J. F. Jardine is Canada Research Chair and
Professor of Mathematics at the University of Western Ontario. He is the author of Generalized Etale Cohomology Theories
and Simplicial Homotopy Theory (with P. Goerss).
  
  Publisher: Springer; 2015
edition (10 June 2015)
  Language: English
  ISBN-10: 1493922998
  ISBN-13: 978-1493922994
  
  
 
 						

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