Globally valued fields: foundations
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916384951238656 |
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| author | Yaacov, Itaï Ben Destic, Pablo Hrushovski, Ehud Szachniewicz, Michał |
| author_facet | Yaacov, Itaï Ben Destic, Pablo Hrushovski, Ehud Szachniewicz, Michał |
| contents | We present foundations of globally valued fields, i.e., of a class of fields with an extra structure, capturing some aspects of the geometry of global fields, based on the product formula. We provide a dictionary between various data defining such extra structure: syntactic (models of some unbounded continuous logic theory), Arakelov theoretic, and measure theoretic. In particular we obtain a representation theorem relating globally valued fields and adelic curves defined by Chen and Moriwaki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04570 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Globally valued fields: foundations Yaacov, Itaï Ben Destic, Pablo Hrushovski, Ehud Szachniewicz, Michał Logic We present foundations of globally valued fields, i.e., of a class of fields with an extra structure, capturing some aspects of the geometry of global fields, based on the product formula. We provide a dictionary between various data defining such extra structure: syntactic (models of some unbounded continuous logic theory), Arakelov theoretic, and measure theoretic. In particular we obtain a representation theorem relating globally valued fields and adelic curves defined by Chen and Moriwaki. |
| title | Globally valued fields: foundations |
| topic | Logic |
| url | https://arxiv.org/abs/2409.04570 |