000 03256nam a22004935i 4500
001 978-3-540-39665-9
003 DE-He213
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007 cr nn 008mamaa
008 121227s2003 gw | s |||| 0|eng d
020 _a9783540396659
_9978-3-540-39665-9
024 7 _a10.1007/b13465
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKS
_2thema
082 0 4 _a514.74
_223
100 1 _aNavarro González, Juan A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aC∞-Differentiable Spaces
_h[electronic resource] /
_cby Juan A. Navarro González, Juan B. Sancho de Salas.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2003.
300 _aXVI, 196 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1824
505 0 _aIntroduction -- 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 Fréchet Modules -- B. Space of Jets -- References -- Index.
520 _aThe 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.
650 0 _aGlobal analysis.
650 0 _aAlgebra.
650 1 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aCommutative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11043
700 1 _aSancho de Salas, Juan B.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540200727
776 0 8 _iPrinted edition:
_z9783662161562
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1824
856 4 0 _uhttps://doi.org/10.1007/b13465
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9794
_d9794