Endomorphisms of power series fields and residue fields of Fargues-Fontaine curves
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- by Kiran S. Kedlaya and Michael Temkin PDF
- Proc. Amer. Math. Soc. 146 (2018), 489-495
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 bijective. As a corollary, we resolve a question of Fargues and Fontaine by showing that for $p$ a prime and $\mathbb {C}_p$ a completed algebraic closure of $\mathbb {Q}_p$, there exist closed points of the Fargues-Fontaine curve associated to $\mathbb {C}_p$ whose residue fields are not (even abstractly) isomorphic to $\mathbb {C}_p$ as topological fields.References
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Additional Information
- Kiran S. Kedlaya
- Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California, 92093
- MR Author ID: 349028
- ORCID: 0000-0001-8700-8758
- Received by editor(s): July 3, 2016
- Received by editor(s) in revised form: March 19, 2017
- Published electronically: August 7, 2017
- Additional Notes: The first author received additional support from NSF grants DMS-1101343 and DMS-1501214 and from UC San Diego (Stefan E. Warschawski Professorship)
The second author was supported by the Israel Science Foundation (grant No. 1159/15)
Some of this work was carried out during the MSRI fall 2014 semester program “New geometric methods in number theory and automorphic forms” supported by NSF grant DMS-0932078 - Communicated by: Romyar T. Sharifi
- © Copyright 2017 Kiran S. Kedlaya and Michael Temkin
- Journal: Proc. Amer. Math. Soc. 146 (2018), 489-495
- MSC (2010): Primary 12J25
- DOI: https://doi.org/10.1090/proc/13818
- MathSciNet review: 3731685