具有全球价值的领域：基础

arXiv - MATH - Logic Pub Date : 2024-09-06 DOI:arxiv-2409.04570

Itaï Ben Yaacov, Pablo Destic, Ehud Hrushovski, Michał Szachniewicz

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引用次数: 0

摘要

我们提出了全局值域的基础，即一类具有额外结构的域的基础，它捕捉了全局域几何的某些方面，并以积公式为基础。我们提供了定义这种额外结构的各种数据之间的字典：句法（某种无界连续逻辑理论的模型）、阿拉克洛夫理论和度量理论。特别是，我们得到了一个与全局有价域和陈和森胁定义的阿德尔曲线相关的表示定理。

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Globally valued fields: foundations

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.

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arXiv - MATH - Logic

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