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arXiv · 1602.09004

On commutative nonarchimedean Banach fields

Kiran S. Kedlaya
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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. 2016-02-29. On commutative nonarchimedean Banach fields. https://arxiv.org/abs/1602.09004

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