Zilber's notion of logically perfect structure: Universal Covers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910538299080704 |
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| author | Baldwin, John T. Villaveces, Andrés |
| author_facet | Baldwin, John T. Villaveces, Andrés |
| contents | We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we discuss in a systematic and unified way several examples indicating the main ideas of the proofs and the necessary changes in method for different situations: exponential covers, modular and Shimura curves, Shimura and abelian varieties, and coherent families of smooth covers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04650 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Zilber's notion of logically perfect structure: Universal Covers Baldwin, John T. Villaveces, Andrés Logic 03C45, 03C64, 03C98, 11U09, 12L12, 03-03, 03C75, 03C48 We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we discuss in a systematic and unified way several examples indicating the main ideas of the proofs and the necessary changes in method for different situations: exponential covers, modular and Shimura curves, Shimura and abelian varieties, and coherent families of smooth covers. |
| title | Zilber's notion of logically perfect structure: Universal Covers |
| topic | Logic 03C45, 03C64, 03C98, 11U09, 12L12, 03-03, 03C75, 03C48 |
| url | https://arxiv.org/abs/2302.04650 |