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

Kiran S. Kedlaya; Michael Temkin

doi:10.1090/proc/13818

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

Kiran S. Kedlaya, Michael Temkin

Research output: Contribution to journal › Article › peer-review

6 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 C_p a completed algebraic closure of Q_p, there exist closed points of the Fargues-Fontaine curve associated to C_p whose residue fields are not (even abstractly) isomorphic to C_p as topological fields.

Original language	English
Pages (from-to)	489-495
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	2
DOIs	https://doi.org/10.1090/proc/13818
State	Published - 2017
Externally published	Yes

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

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

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