Author	Navarro Gonzรกlez, Juan A. author
Title	Cโ-Differentiable Spaces [electronic resource] / by Juan A. Navarro Gonzรกlez, Juan B. Sancho de Salas
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2003
Connect to	http://dx.doi.org/10.1007/b13465
Descript	XVI, 196 p. online resource

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 Frรฉchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of Ĉ\infinity-rings and Ĉ\infinity-schemes, as well as in the framework of Spallek's Ĉ\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Frรฉchet spaces

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 Frรฉchet Modules -- B. Space of Jets -- References -- Index

1. Mathematics
2. Commutative algebra
3. Commutative rings
4. Global analysis (Mathematics)
5. Manifolds (Mathematics)
6. Mathematics
7. Global Analysis and Analysis on Manifolds
8. Commutative Rings and Algebras