Cargando…
Algebraic geometry over C[infinity]-rings /
"If X is a manifold then the R-algebra C[infinity](X) of smooth functions C : X [right arrow] R is a C[infinity]-ring. That is, for each smooth function f : Rn [right arrow] R there is an n-fold operation]Phi]f : C[infinity](X)n [right arrow] C[infinity](X) acting by [Phi]f : (c1 ..., cn) [righ...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI, USA :
American Mathematical Society,
[2019]
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1256. |
| Temas: |
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}
> General theory of differentiable manifolds [See also 32Cxx]
|
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_on1125343181 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 191030t20192019riua ob 001 0 eng d | ||
| 040 | |a GZM |b eng |e pn |c GZM |d YDXIT |d N$T |d OCL |d UKAHL |d SFB |d UX1 |d VT2 |d K6U |d OCLCO |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d S9M |d OCLCL | ||
| 019 | |a 1266286673 | ||
| 020 | |a 1470453363 |q (electronic book) | ||
| 020 | |a 9781470453367 |q (electronic bk.) | ||
| 020 | |a 1470436450 | ||
| 020 | |a 9781470436452 | ||
| 020 | |z 9781470436452 | ||
| 029 | 1 | |a AU@ |b 000069523899 | |
| 035 | |a (OCoLC)1125343181 |z (OCoLC)1266286673 | ||
| 050 | 4 | |a QA614.3 |b .J69 2019 | |
| 082 | 0 | 4 | |a 516.3/6 |2 23 |
| 084 | |a 58A40 |a 14A20 |a 46E25 |a 51K10 |2 msc | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Joyce, Dominic D., |e author. | |
| 245 | 1 | 0 | |a Algebraic geometry over C[infinity]-rings / |c Dominic Joyce. |
| 246 | 3 | |a Algebraic geometry over C infinity-rings | |
| 264 | 1 | |a Providence, RI, USA : |b American Mathematical Society, |c [2019] | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource (v, 139 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 260, number 1256 | |
| 500 | |a "July 2019, Volume 260, Number 1256 (fifth of 5 numbers)." | ||
| 500 | |a Title page displays an infinity sign rather than the word "infinity." | ||
| 504 | |a Includes bibliographical references (pages 131-133) and index. | ||
| 588 | 0 | |a Online resource, title from digital title page (viewed on September 16, 2020). | |
| 505 | 0 | |a C[infinity]-rings -- The C[infinity]-ring C[infinity](X) of a manifold X -- C[infinity]-ringed spaces and C[infinity]-schemes -- Modules over C[infinity]-rings and C[infinity]-schemes -- C[infinity]-stacks -- Deligne-Mumford C[infinity]-stacks -- Sheaves on Deligne-Mumford C[infinity]-stacks -- Orbifold strata of C[infinity]-stacks. | |
| 520 | |a "If X is a manifold then the R-algebra C[infinity](X) of smooth functions C : X [right arrow] R is a C[infinity]-ring. That is, for each smooth function f : Rn [right arrow] R there is an n-fold operation]Phi]f : C[infinity](X)n [right arrow] C[infinity](X) acting by [Phi]f : (c1 ..., cn) [right arrow] f(c1 ..., cn), and these operations [Phi]f satisfy many natural identities. Thus, C[infinity](X) actually has a far richer structure than the obvious R-algebra structure. We explain the foundations of a version of algebraic geometry in which rings or algebras are replaced by C[infinity]-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C[infinity]-schemes, a category of geometric objects which generalize manifolds, and whose morphisms generalize smooth maps. We also study quasicoherent sheaves on C[infinity]-schemes, and C[infinity]-stacks, in particular Deligne- Mumford C[infinity]-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C[infinity]-rings and C[infinity]-schemes have long been part of synthetic differential geometry. But we develop them in new directions. In Joyce (2014, 2012, 2012 preprint), the author uses these tools to define d-manifolds and d-orbifolds, 'derived' versions of manifolds and orbifolds related to Spivak's 'derived manifolds' (2010)"-- |c Provided by publisher | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Differentiable functions. | |
| 650 | 0 | |a Smooth affine curves. | |
| 650 | 0 | |a Rings (Algebra) | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 6 | |a Fonctions différentiables. | |
| 650 | 6 | |a Courbes affines lisses. | |
| 650 | 6 | |a Anneaux (Algèbre) | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 7 | |a Geometría algebraica |2 embne | |
| 650 | 7 | |a Anillos (Álgebra) |2 embne | |
| 650 | 0 | 7 | |a Funciones diferenciables |2 embucm |
| 650 | 7 | |a Smooth affine curves |2 fast | |
| 650 | 7 | |a Rings (Algebra) |2 fast | |
| 650 | 7 | |a Geometry, Algebraic |2 fast | |
| 650 | 7 | |a Differentiable functions |2 fast | |
| 650 | 7 | |a Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} |x General theory of differentiable manifolds [See also 32Cxx] |2 msc | |
| 650 | 7 | |a Algebraic geometry |x Foundations |x Generalizations (algebraic spaces, stacks) |2 msc | |
| 650 | 7 | |a Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} |x Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10} |2 msc | |
| 650 | 7 | |a Geometry {For algebraic geometry, see 14-XX} |x Distance geometry |x Synthetic differential geometry. |2 msc | |
| 758 | |i has work: |a Algebraic geometry over C[infinity]-rings (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFXj4hxj9mqhW97jmqBgKd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t Algebraic geometry over C infinity rings. |d Providence, RI, USA : American Mathematical Society, [2019] |z 9781470436452 |w (OCoLC)1119590354 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1256. |x 0065-9266 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5904555 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445285 | ||
| 938 | |a EBSCOhost |b EBSC |n 2256054 | ||
| 994 | |a 92 |b IZTAP | ||