C [infinity]-differentiable spaces /
The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer-Verlag,
[2003]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1824. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Frchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^ infinity-rings and C^ infinity-schemes, as well as in the framework of Spalleks C^ infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Frchet spaces. |
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| Item Description: | On title page [infinity] appears as the infinity symbol at superscript position. Electronic resource. |
| Physical Description: | 1 online resource (xiii, 188 pages) |
| Bibliography: | Includes bibliographical references (pages [181]-183) and index. |
| ISBN: | 9783540396659 (electronic bk.) 3540396659 (electronic bk.) |
| ISSN: | 0075-8434 ; |