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 |
| Sumario: | "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)"-- |
|---|---|
| Notas: | "July 2019, Volume 260, Number 1256 (fifth of 5 numbers)." Title page displays an infinity sign rather than the word "infinity." |
| Descripción Física: | 1 online resource (v, 139 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 131-133) and index. |
| ISBN: | 1470453363 9781470453367 1470436450 9781470436452 |
| ISSN: | 0065-9266 ; |