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Local homotopy theory [electronic resource]

Local homotopy theory [electronic resource]

자료유형
E-Book(소장)
개인저자
Jardine, J. F., 1951-.
서명 / 저자사항
Local homotopy theory [electronic resource] / John F. Jardine.
발행사항
New York, NY :   Springer New York :   Imprint: Springer,   2015.  
형태사항
1 online resource (ix, 508 p.) : ill.
기타형태 저록
Print version   Local homotopy theory.   New York : Springer, 2015   9781493922994   (211009)000045863580  
총서사항
Springer monographs in mathematics,1439-7382
ISBN
9781493923007
요약
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Homotopy theory.
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020 ▼a 9781493923007
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050 0 0 ▼a QA612.7
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100 1 ▼a Jardine, J. F., ▼d 1951-.
245 1 0 ▼a Local homotopy theory ▼h [electronic resource] / ▼c John F. Jardine.
260 ▼a New York, NY : ▼b Springer New York : ▼b Imprint: Springer, ▼c 2015.
300 ▼a 1 online resource (ix, 508 p.) : ▼b ill.
490 1 ▼a Springer monographs in mathematics, ▼x 1439-7382
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a 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.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Homotopy theory.
776 0 8 ▼i Print version ▼t Local homotopy theory. ▼d New York : Springer, 2015 ▼z 9781493922994 ▼w (211009)000045863580
830 0 ▼a Springer monographs in mathematics.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-1-4939-2300-7
945 ▼a KLPA
991 ▼a E-Book(소장)

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