C∞-differentiable spaces
著者
書誌事項
C∞-differentiable spaces
（Lecture notes in mathematics, 1824）
Springer-Verlag, c2003
- タイトル別名
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C [infinity] -differentiable spaces
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注記
On t.p. [infinity] appears as the inifinity symbol at superscript position
Includes bibliographical references (p. [181]-183) and index
内容説明・目次
内容説明
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 Frechet 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 Spallek's C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Frechet spaces.
目次
Introduction.- 1. Differentiable Manifolds.- 2. Differentiable Algebras.- 3. Differentiable Spaces.- 4. Topology of Differentiable Spaces.- 5. Embeddings.- 6. Topological Tensor Products.- 7. Fibred Products.- 8. Topological Localization.- 9. Finite Morphisms.- 10. Smooth Morphisms.- 11. Quotients by Compact Lie Groups.- A. Sheaves of Frechet Modules.- B. Space of Jets.- References.- Index.
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