Category-theoretic Reconstruction of Log Schemes from Categories of Reduced fs Log Schemes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929216415596544 |
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| author | Yuji, Tomoki |
| author_facet | Yuji, Tomoki |
| contents | Let $S^{\log}$ be a locally Noetherian fs log scheme and $\blacklozenge/S^{\log}$ a set of properties of fs log schemes over $S^{\log}$. In the present paper, we shall mainly be concerned with the properties "reduced", "quasi-compact over $S^{\log}$", "quasi-separated over $S^{\log}$", "separated over $S^{\log}$", and "of finite type over $S^{\log}$". We shall write $\mathsf{Sch}_{\blacklozenge/S^{\log}}$ for the full subcategory of the category of fs log schemes over $S^{\log}$ determined by the fs log schemes over $S^{\log}$ that satisfy every property contained in $\blacklozenge/S^{\log}$. In the present paper, we discuss a purely category-theoretic reconstruction of the log scheme $S^{\log}$ from the intrinsic structure of the abstract category $\mathsf{Sch}_{\blacklozenge/S^{\log}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01787 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Category-theoretic Reconstruction of Log Schemes from Categories of Reduced fs Log Schemes Yuji, Tomoki Algebraic Geometry Category Theory 14A21 (primary) 14L15, 14L35 (secondary) Let $S^{\log}$ be a locally Noetherian fs log scheme and $\blacklozenge/S^{\log}$ a set of properties of fs log schemes over $S^{\log}$. In the present paper, we shall mainly be concerned with the properties "reduced", "quasi-compact over $S^{\log}$", "quasi-separated over $S^{\log}$", "separated over $S^{\log}$", and "of finite type over $S^{\log}$". We shall write $\mathsf{Sch}_{\blacklozenge/S^{\log}}$ for the full subcategory of the category of fs log schemes over $S^{\log}$ determined by the fs log schemes over $S^{\log}$ that satisfy every property contained in $\blacklozenge/S^{\log}$. In the present paper, we discuss a purely category-theoretic reconstruction of the log scheme $S^{\log}$ from the intrinsic structure of the abstract category $\mathsf{Sch}_{\blacklozenge/S^{\log}}$. |
| title | Category-theoretic Reconstruction of Log Schemes from Categories of Reduced fs Log Schemes |
| topic | Algebraic Geometry Category Theory 14A21 (primary) 14L15, 14L35 (secondary) |
| url | https://arxiv.org/abs/2212.01787 |