Univalent Foundations of Constructive Algebraic Geometry
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.17362
- arXiv:
- arXiv:2407.17362
- Bibcode:
- 2024arXiv240717362Z
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Logic
- E-Print:
- 53 pages