Local Homotopy Theory
The subject of this monograph is the homotopy theory of diagrams of spaces, chain complexes, spectra, and generalized spectra, where the homotopy types are determined locally by a Grothendieck topology. The main components of the theory are the local homotopy theories of simplicial presheaves an...
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2015
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57251 |
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oai:scholar.dlu.edu.vn:DLU123456789-572512023-11-11T05:43:22Z Local Homotopy Theory Jardine, John F Homotopy Theory The subject of this monograph is the homotopy theory of diagrams of spaces, chain complexes, spectra, and generalized spectra, where the homotopy types are determined locally by a Grothendieck topology. The main components of the theory are the local homotopy theories of simplicial presheaves and simplicial sheaves, local stable homotopy theories, derived cate gories, and non-abelian cohomology theory. This book presents formal descriptions of the structures comprising these theories, and the links between them. Examples and sample calculations are provided, along with some commentary. The subject has broad applicability. It can be used to study presheaf and sheaf objects which are defined on the open subsets of a topological space, or on the open subschemes of a scheme, or on more exotic covers. Local homotopy theory is a foundational tool for motivic homotopy theory, and for the theory of topological modular forms in classical stable homotopy theory. As such, there are continuing applications of the theory in topology, geometry, and number theory. The applications and extensions of the subject comprise a large and expanding literature, in multiple subject areas... 2015-08-07T01:24:12Z 2015-08-07T01:24:12Z 2015 Book 978-1-4939-2300-7 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57251 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Homotopy Theory |
| spellingShingle |
Homotopy Theory Jardine, John F Local Homotopy Theory |
| description |
The subject of this monograph is the homotopy theory of diagrams of spaces,
chain complexes, spectra, and generalized spectra, where the homotopy types are
determined locally by a Grothendieck topology.
The main components of the theory are the local homotopy theories of simplicial
presheaves and simplicial sheaves, local stable homotopy theories, derived cate
gories, and non-abelian cohomology theory. This book presents formal descriptions
of the structures comprising these theories, and the links between them. Examples
and sample calculations are provided, along with some commentary.
The subject has broad applicability. It can be used to study presheaf and sheaf
objects which are defined on the open subsets of a topological space, or on the open
subschemes of a scheme, or on more exotic covers. Local homotopy theory is a
foundational tool for motivic homotopy theory, and for the theory of topological
modular forms in classical stable homotopy theory. As such, there are continuing
applications of the theory in topology, geometry, and number theory. The applications
and extensions of the subject comprise a large and expanding literature, in multiple
subject areas... |
| format |
Book |
| author |
Jardine, John F |
| author_facet |
Jardine, John F |
| author_sort |
Jardine, John F |
| title |
Local Homotopy Theory |
| title_short |
Local Homotopy Theory |
| title_full |
Local Homotopy Theory |
| title_fullStr |
Local Homotopy Theory |
| title_full_unstemmed |
Local Homotopy Theory |
| title_sort |
local homotopy theory |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57251 |
| _version_ |
1782536181539405824 |