Globally valued fields: foundations
Logic
2024-09-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2409.04570,
title = {Globally valued fields: foundations},
author = {Itaï Ben Yaacov and Pablo Destic and Ehud Hrushovski and Michał Szachniewicz},
journal= {arXiv preprint arXiv:2409.04570},
year = {2024}
}
Comments
51 pages