Basic constructions over C∞-schemes
C∞-Rings are R-algebras equipped with operations φf for every f ∈ C∞(Rn) and every n ∈ N. Therefore, a C∞-version of algebraic geometry can be developed using C∞-rings instead of ordinary rings and many classical constructions can be performed in this context. In particular, C∞-schemes are the C∞ co...
- Autores:
-
Hernández Rizzo, Pedro Jesús
Olarte Sepulveda, Cristian Danilo
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2023
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/46234
- Acceso en línea:
- https://hdl.handle.net/10495/46234
- Palabra clave:
- Esquemas (Geometría algebraica)
Schemes (Algebraic geometry)
Geometría algebraica
Geometry, algebraic
Anillos (Álgebra)
Rings (algebra)
Variedades de Grassmann
Grassmann manifolds
http://id.loc.gov/authorities/subjects/sh85118107
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| Summary: | C∞-Rings are R-algebras equipped with operations φf for every f ∈ C∞(Rn) and every n ∈ N. Therefore, a C∞-version of algebraic geometry can be developed using C∞-rings instead of ordinary rings and many classical constructions can be performed in this context. In particular, C∞-schemes are the C∞ counterpart of classical schemes. Examples of schemes are often obtained by gluing schemes or using fiber products. Another useful way to give examples of schemes is looking for representable functors F : Schemes → Sets. In this work, we show that constructions such as gluing schemes and fiber products can be done in the context of C∞-algebraic geometry and they can be used to exhibit some examples of C∞-schemes such as projective spaces and Grassmannians as well as necessary and sufficient conditions for a functor F : C∞ − Schemes → Sets to be representable. |
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