The Resource Local homotopy theory, John F. Jardine

Local homotopy theory, John F. Jardine

Label
Local homotopy theory
Title
Local homotopy theory
Statement of responsibility
John F. Jardine
Creator
Author
Subject
Genre
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, 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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorDate
1951-
http://library.link/vocab/creatorName
Jardine, J. F.
Dewey number
514/.24
Index
index present
LC call number
QA612.7
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Springer monographs in mathematics
http://library.link/vocab/subjectName
  • Homotopy theory
  • MATHEMATICS
  • Homotopy theory
  • Mathematics
  • Category Theory, Homological Algebra
  • K-Theory
  • Algebraic Topology
  • Algebraic topology
  • Mathematical foundations
Label
Local homotopy theory, John F. Jardine
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-1-4939-2300-7
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
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 Non-abelian cohomology -- Part IV Stable homotopy theory -- 10 Spectra and T-spectra -- 11 Symmetric T-spectra -- References -- Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781493922994
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
SpringerLink
Other control number
10.1007/978-1-4939-2300-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)910324356
  • (OCoLC)ocn910324356
Label
Local homotopy theory, John F. Jardine
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-1-4939-2300-7
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
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 Non-abelian cohomology -- Part IV Stable homotopy theory -- 10 Spectra and T-spectra -- 11 Symmetric T-spectra -- References -- Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781493922994
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
SpringerLink
Other control number
10.1007/978-1-4939-2300-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)910324356
  • (OCoLC)ocn910324356

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