Journal Article

Noetherian Properties of Fargues-Fontaine Curves

Kiran S. Kedlaya

in International Mathematics Research Notices

Volume 2016, issue 8, pages 2544-2567
Published in print January 2016 | ISSN: 1073-7928
Published online July 2015 | e-ISSN: 1687-0247 | DOI:
Noetherian Properties of Fargues-Fontaine Curves

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We establish that the extended Robba rings associated to a perfect nonarchimedean field of characteristic [math], which arise in [math]-adic Hodge theory as certain completed localizations of the ring of Witt vectors, are strongly noetherian Banach rings; that is, the completed polynomial ring in any number of variables over such a Banach ring is noetherian. This enables Huber's theory of adic spaces to be applied to such rings. We also establish that rational localizations of these rings are principal ideal domains and that étale covers of these rings (in the sense of Huber) are Dedekind domains.

Journal Article.  10326 words.  Illustrated.

Subjects: Mathematics ; Pure Mathematics

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