The Resource Local Homotopy Theory, by John F. Jardine, (electronic resource)
Local Homotopy Theory, by John F. Jardine, (electronic resource)
Resource Information
The item Local Homotopy Theory, by John F. Jardine, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Local Homotopy Theory, by John F. Jardine, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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, nonabelian 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 Ktheory. 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
 Language
 eng
 Extent
 IX, 508 p. 514 illus.
 Contents

 Preface
 1 Introduction
 Part I Preliminaries
 2 Homotopy theory of simplicial sets
 3 Some topos theory
 Part II Simplicial presheaves and simplicial sheaves
 4 Local weak equivalences
 5 Local model structures
 6 Cocycles
 7 Localization theories
 Part III Sheaf cohomology theory
 8 Homology sheaves and cohomology groups
 9 Nonabelian cohomology
 Part IV Stable homotopy theory
 10 Spectra and Tspectra
 11 Symmetric Tspectra
 References
 Index
 Isbn
 9781493923007
 Label
 Local Homotopy Theory
 Title
 Local Homotopy Theory
 Statement of responsibility
 by John F. Jardine
 Language
 eng
 Summary
 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, nonabelian 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 Ktheory. 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
 http://library.link/vocab/creatorName
 Jardine, John F
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Category theory (Mathematics)
 Homological algebra
 Ktheory
 Algebraic topology
 Label
 Local Homotopy Theory, by John F. Jardine, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Preface  1 Introduction  Part I Preliminaries  2 Homotopy theory of simplicial sets  3 Some topos theory  Part II Simplicial presheaves and simplicial sheaves  4 Local weak equivalences  5 Local model structures  6 Cocycles  7 Localization theories  Part III Sheaf cohomology theory  8 Homology sheaves and cohomology groups  9 Nonabelian cohomology  Part IV Stable homotopy theory  10 Spectra and Tspectra  11 Symmetric Tspectra  References  Index
 Control code
 9781493923007
 Dimensions
 unknown
 Extent
 IX, 508 p. 514 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781493923007
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9781493923007
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086547379
 Label
 Local Homotopy Theory, by John F. Jardine, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Preface  1 Introduction  Part I Preliminaries  2 Homotopy theory of simplicial sets  3 Some topos theory  Part II Simplicial presheaves and simplicial sheaves  4 Local weak equivalences  5 Local model structures  6 Cocycles  7 Localization theories  Part III Sheaf cohomology theory  8 Homology sheaves and cohomology groups  9 Nonabelian cohomology  Part IV Stable homotopy theory  10 Spectra and Tspectra  11 Symmetric Tspectra  References  Index
 Control code
 9781493923007
 Dimensions
 unknown
 Extent
 IX, 508 p. 514 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781493923007
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9781493923007
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086547379
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/LocalHomotopyTheorybyJohnF.Jardine/MIU8U6VWs/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/LocalHomotopyTheorybyJohnF.Jardine/MIU8U6VWs/">Local Homotopy Theory, by John F. Jardine, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>