Japanese Dedekind domains are excellent
Number Theory
2022-05-10 v3
Abstract
The well-known fundamental identity in number theory expresses the degree of an extension of global fields in terms of local information. In this article we show a generalized fundamental identity for arbitrary Dedekind domains. As an application, we show that any Japanese Dedekind domain is already excellent.
Cite
@article{arxiv.2102.10481,
title = {Japanese Dedekind domains are excellent},
author = {Chia-Fu Yu},
journal= {arXiv preprint arXiv:2102.10481},
year = {2022}
}
Comments
Title changed; add the exposition of valuation theory (Section 3 of v1) back; to appear in Taiwanese J. Math.; comments are welcome