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 Fréchet 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 Fréchet spaces.
C^\infinity - Differentiable Spaces
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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 Fréchet 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 Fréchet spaces.
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First Sentence:
The notion of smooth manifold, as well as those of analytic manifold and scheme, may be expressed appropriately in the language of ringed spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
differentiable algebra, differentiable subspace, reduced ringed spaces, smooth manifold whose topology, separated smooth manifold, differentiable spaces, categorial quotient, equivariant embedding theorem, open epimorphism, differentiable action, final topology induced, tangent linear map, closed smooth submanifold, finite flat morphism, affine open cover, localization topology, geometric quotient, differentiable group, locally ringed, fibred products, surjective submersion, continuous morphisms, universal morphism, canonical topology, space whose topology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fréchet A-module New!
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The notion of smooth manifold, as well as those of analytic manifold and scheme, may be expressed appropriately in the language of ringed spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
differentiable algebra, differentiable subspace, reduced ringed spaces, smooth manifold whose topology, separated smooth manifold, differentiable spaces, categorial quotient, equivariant embedding theorem, open epimorphism, differentiable action, final topology induced, tangent linear map, closed smooth submanifold, finite flat morphism, affine open cover, localization topology, geometric quotient, differentiable group, locally ringed, fibred products, surjective submersion, continuous morphisms, universal morphism, canonical topology, space whose topology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fréchet A-module New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 92
books:
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- Forward-Backward Stochastic Differential Equations and their Applications (Lecture Notes in Mathematics) by Jin Ma in Back Matter (1), and Back Matter (2)
- Geometric Curve Evolution and Image Processing (Lecture Notes in Mathematics) by Frédéric Cao in Back Matter
- Grothendieck Duality and Base Change (Lecture Notes in Mathematics) by Brian Conrad in Back Matter
- Notes on Infinite Permutation Groups (Lecture Notes in Mathematics) by Meenaxi Bhattacharjee in Back Matter
- Elemental Methods in Ergodic Ramsey Theory by Randall McCutcheon in Back Matter
See all 92 books this book cites
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