大葉大學圖書館 |

Local homotopy theory[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	514.24
書名/作者:	Local homotopy theory/ by John F. Jardine.
作者:	Jardine, John F.
出版者:	New York, NY : : Springer New York :, 2015.
面頁冊數:	ix, 508 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Homotopy theory.
標題:	Mathematics.
標題:	Category Theory, Homological Algebra.
標題:	K-Theory.
標題:	Algebraic Topology.
ISBN:	9781493923007 (electronic bk.)
ISBN:	9781493922994 (paper)
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-1-4939-2300-7

Local homotopy theory[electronic resource] /
Jardine, John F.

Local homotopy theory[electronic resource] /by John F. Jardine. - New York, NY :Springer New York :2015. - ix, 508 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

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.

ISBN: 9781493923007 (electronic bk.)

Standard No.: 10.1007/978-1-4939-2300-7doiSubjects--Topical Terms:

465831
Homotopy theory.

LC Class. No.: QA612.7

Dewey Class. No.: 514.24

Local homotopy theory[electronic resource] /
LDR:02847nmm a2200337 a 4500 001 438979
003 DE-He213
005 20160105091932.0
006 m d
007 cr nn 008maaau
008 160315s2015 nyu s 0 eng d
020 $a 9781493923007 (electronic bk.)
020 $a 9781493922994 (paper)
024 7 $a 10.1007/978-1-4939-2300-7 $2 doi
035 $a 978-1-4939-2300-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612.7
072 7 $a PBC $2 bicssc
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 514.24 $2 23
090 $a QA612.7 $b .J37 2015
100 1 $a Jardine, John F. $3 626538
245 1 0 $a Local homotopy theory $h [electronic resource] / $c by John F. Jardine.
260 $a New York, NY : $b Springer New York : $b Imprint: Springer, $c 2015.
300 $a ix, 508 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
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.
650 0 $a Homotopy theory. $3 465831
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Category Theory, Homological Algebra. $3 464923
650 2 4 $a K-Theory. $3 470906
650 2 4 $a Algebraic Topology. $3 464924
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 464117
856 4 0 $u http://dx.doi.org/10.1007/978-1-4939-2300-7
950 $a Mathematics and Statistics (Springer-11649)