JournalsdmVol. 23pp. 171–188

On Commutative Nonarchimedean Banach Fields

  • Kiran S. Kedlaya

    Dept. of Mathematics, University of California, San Diego, 9500 Gilman Drive 0112, La Jolla, CA 92093, USA
On Commutative Nonarchimedean Banach Fields cover
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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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Kiran S. Kedlaya, On Commutative Nonarchimedean Banach Fields. Doc. Math. 23 (2018), pp. 171–188

DOI 10.4171/DM/616