On commutative nonarchimedean Banach fields
Number Theory
2019-08-30 v7
Abstract
We study the problem of whether a commutative nonarchimedean Banach ring which is algebraically a field can be topologized by a multiplicative norm. This can fail in general, but it holds for uniform Banach rings under some mild extra conditions. Notably, any perfectoid ring whose underlying ring is a field is a perfectoid field.
Keywords
Cite
@article{arxiv.1602.09004,
title = {On commutative nonarchimedean Banach fields},
author = {Kiran S. Kedlaya},
journal= {arXiv preprint arXiv:1602.09004},
year = {2019}
}
Comments
14 pages; v7: includes corrections to published version