On commutative nonarchimedean Banach fields

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.

14 pages; v7: includes corrections to published version

References in corpus (3)

• Integral p-adic Hodge theory
• Relative p-adic Hodge theory, II: Imperfect period rings
• An Open Mapping Theorem for rings which have a zero sequence of units

Cited by in corpus (1)

• Topological spectrum and perfectoid Tate rings