7. On Nonarchimedean Banach Fields

  • Kiran S. Kedlaya Dept. of Mathematics, University of California, San Diego, 9500 Gilman Drive 0112, La Jolla, CA 92093, USA
Keywords: nonarchimedean Banach rings, perfectoid 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.

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Published
2018-05-04
Section
Unassigned Articles