Endomorphisms of power series fields and residue fields of fargues-fontaine curves

Kiran S. Kedlaya, Michael Temkin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We show that for k a perfect field of characteristic p, there exist endomorphisms of the completed algebraic closure of k((t)) which are not bijec-tive. As a corollary, we resolve a question of Fargues and Fontaine by showing that for p a prime and Cp a completed algebraic closure of Qp, there exist closed points of the Fargues-Fontaine curve associated to Cp whose residue fields are not (even abstractly) isomorphic to Cp as topological fields.

Original languageAmerican English
Pages (from-to)489-495
Number of pages7
JournalProceedings of the American Mathematical Society
Volume146
Issue number2
DOIs
StatePublished - 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Kiran S. Kedlaya and Mihael Temkin.

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