Univalent Foundations of Constructive Algebraic Geometry
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917732021174272 |
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| author | Zeuner, Max |
| author_facet | Zeuner, Max |
| contents | We investigate two constructive approaches to defining quasi-compact and quasi-separated schemes (qcqs-schemes), namely qcqs-schemes as locally ringed lattices and as functors from rings to sets. We work in Homotopy Type Theory and Univalent Foundations, but reason informally. The main result is a constructive and univalent proof that the two definitions coincide, giving an equivalence between the respective categories of qcqs-schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Univalent Foundations of Constructive Algebraic Geometry Zeuner, Max Algebraic Geometry Logic We investigate two constructive approaches to defining quasi-compact and quasi-separated schemes (qcqs-schemes), namely qcqs-schemes as locally ringed lattices and as functors from rings to sets. We work in Homotopy Type Theory and Univalent Foundations, but reason informally. The main result is a constructive and univalent proof that the two definitions coincide, giving an equivalence between the respective categories of qcqs-schemes. |
| title | Univalent Foundations of Constructive Algebraic Geometry |
| topic | Algebraic Geometry Logic |
| url | https://arxiv.org/abs/2407.17362 |