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

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

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

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/proc/13818

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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.",

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AB - 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.

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DO - 10.1090/proc/13818

M3 - مقالة

SN - 0002-9939

VL - 146

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EP - 495

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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