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Globally valued fields: foundations
- Publication Year :
- 2024
-
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.<br />Comment: 51 pages
- Subjects :
- Mathematics - Logic
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.04570
- Document Type :
- Working Paper