On Nonarchimedean Banach Fields
Kiran S. Kedlaya
Dept. of Mathematics, University of California, San Diego, 9500 Gilman Drive 0112, La Jolla, CA 92093, USA
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.
Cite this article
Kiran S. Kedlaya, On Nonarchimedean Banach Fields. Doc. Math. 23 (2018), pp. 171–188
DOI 10.4171/DM/616