LEADER 03673nam 22006495 450 001 996466504503316 005 20200701014514.0 010 $a3-540-39665-9 024 7 $a10.1007/b13465 035 $a(CKB)1000000000230811 035 $a(SSID)ssj0000392784 035 $a(PQKBManifestationID)12104491 035 $a(PQKBTitleCode)TC0000392784 035 $a(PQKBWorkID)10361415 035 $a(PQKB)10618320 035 $a(DE-He213)978-3-540-39665-9 035 $a(MiAaPQ)EBC5595467 035 $a(PPN)237972794 035 $a(EXLCZ)991000000000230811 100 $a20121227d2003 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aC^\infinity - Differentiable Spaces$b[electronic resource] /$fby Juan A. Navarro González, Juan B. Sancho de Salas 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (XVI, 196 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1824 300 $aIncludes index. 311 $a3-540-20072-X 327 $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. 330 $aThe volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek?s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1824 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aCommutative algebra 606 $aCommutative rings 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aCommutative Rings and Algebras. 676 $a516.36 700 $aNavarro González$b Juan A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478885 702 $aSancho de Salas$b Juan B$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466504503316 996 $aC^\infinity - Differentiable Spaces$92524127 997 $aUNISA