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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.15631 |
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| _version_ | 1866929226264870912 |
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| author | Chacón, Andrés Ramírez, María Camila Reyes, Armando |
| author_facet | Chacón, Andrés Ramírez, María Camila Reyes, Armando |
| contents | Motivated by Smith's work \cite{Smith2003, Smith2016} on maps between non-commu\-tative projective spaces of the form ${\rm Proj}_{nc} A$ in the setting of non-commutative projective geometry developed by Rosenberg and Van den Bergh, and the notion of schematicness introduced by Van Oystaeyen and Willaert \cite{VanOystaeyenWillaert1995} to $\mathbb{N}$-graded rings with the aim of formulating a non-commutative scheme theory à la Grothendieck \cite{EGAII1961}, in this paper we consider a first approach to maps in the Smith's sense in the more general setting of non-commutative projective spaces over semi-graded rings defined by Lezama and Latorre \cite{LezamaLatorre2017}. We extend Smith's key result \cite[Theorem 3.2]{Smith2003}, \cite[Theorem 1.2]{Smith2016} from the category of schematic $\mathbb{N}$-graded rings to the category of schematic semi-graded rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maps between schematic semi-graded rings Chacón, Andrés Ramírez, María Camila Reyes, Armando Algebraic Geometry Quantum Algebra 14A22, 16S38, 16S80, 16U20, 16W60 Motivated by Smith's work \cite{Smith2003, Smith2016} on maps between non-commu\-tative projective spaces of the form ${\rm Proj}_{nc} A$ in the setting of non-commutative projective geometry developed by Rosenberg and Van den Bergh, and the notion of schematicness introduced by Van Oystaeyen and Willaert \cite{VanOystaeyenWillaert1995} to $\mathbb{N}$-graded rings with the aim of formulating a non-commutative scheme theory à la Grothendieck \cite{EGAII1961}, in this paper we consider a first approach to maps in the Smith's sense in the more general setting of non-commutative projective spaces over semi-graded rings defined by Lezama and Latorre \cite{LezamaLatorre2017}. We extend Smith's key result \cite[Theorem 3.2]{Smith2003}, \cite[Theorem 1.2]{Smith2016} from the category of schematic $\mathbb{N}$-graded rings to the category of schematic semi-graded rings. |
| title | Maps between schematic semi-graded rings |
| topic | Algebraic Geometry Quantum Algebra 14A22, 16S38, 16S80, 16U20, 16W60 |
| url | https://arxiv.org/abs/2401.15631 |