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arXiv · 2409.04570

Globally valued fields: foundations

Itaï Ben Yaacov·Pablo Destic·Ehud Hrushovski·Michał Szachniewicz
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Abstract

We present foundations for globally valued fields, a class of enriched fields capturing some aspects of the geometry of global fields, based on the product formula. We show that this class is axiomatizable in the framework of unbounded continuous logic, opening the way to decidability and transfer theorems. We provide a dictionary between various data defining such extra structure: syntactic, Arakelov or cycle-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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Itaï Ben Yaacov, Pablo Destic, Ehud Hrushovski, Michał Szachniewicz. 2024-09-06. Globally valued fields: foundations. https://arxiv.org/abs/2409.04570

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