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∞ 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.

• 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/