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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2511.03433 |
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| _version_ | 1866917062460309504 |
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| author | Siqveland, Arvid |
| author_facet | Siqveland, Arvid |
| contents | In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple modules to construct associative schemes. Here, we consider a commutative ring for which we can use the localization in maximal ideals as local moduli. This gives a categorical definition of schemes that is equivalent to the definition in Hartshorne's book, Algebraic Geometry, 1977. The definition includes a construction of the sheaf associated to a presheaf using projective limits, and this makes the basic results in scheme theory more natural. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical construction of Schemes Siqveland, Arvid Algebraic Geometry 14A15 In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple modules to construct associative schemes. Here, we consider a commutative ring for which we can use the localization in maximal ideals as local moduli. This gives a categorical definition of schemes that is equivalent to the definition in Hartshorne's book, Algebraic Geometry, 1977. The definition includes a construction of the sheaf associated to a presheaf using projective limits, and this makes the basic results in scheme theory more natural. |
| title | Categorical construction of Schemes |
| topic | Algebraic Geometry 14A15 |
| url | https://arxiv.org/abs/2511.03433 |