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


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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How to Cite
KEDLAYA, Kiran S.. 7. On Nonarchimedean Banach Fields. DOCUMENTA MATHEMATICA, [S.l.], v. 23, p. 171-188, may 2018. ISSN 1431-0643. Available at: <https://ojs.elibm.org/index.php/dm/article/view/359>. Date accessed: 23 may 2018. doi: https://doi.org/10.25537/dm.2018v23.171-188.
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