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November 2019 Topics in the anabelian geometry of mixed-characteristic local fields
Yuichiro Hoshi
Hiroshima Math. J. 49(3): 323-398 (November 2019). DOI: 10.32917/hmj/1573787035

Abstract

In the present paper, we study the anabelian geometry of mixedcharacteristic local fields by an algorithmic approach. We begin by discussing some generalities on log-shells of mixed-characteristic local fields. One main topic of this discussion is the difference between the log-shell and the ring of integers. This discussion concerning log-shells allows one to establish mono-anabelian reconstruction algorithms for constructing some objects related to the $p$-adic valuations. Next, we consider open homomorphisms between profinite groups of MLF-type. This consideration leads us to a bi-anabelian result for absolutely unramified mixed-characteristic local fields. Next, we establish some mono-anabelian reconstruction algorithms related to each of absolutely abelian mixed-characteristic local fields, mixed-characteristic local fields of degree one, and Galois-specifiable mixed-characteristic local fields. For instance, we give a mono-anabelian reconstruction algorithm for constructing the Norm map with respect to the finite extension determined by the uniquely determined minimal mixed-characteristic local subfield. Finally, we apply various results of the present paper to prove some facts concerning outer automorphisms of the absolute Galois groups of mixedcharacteristic local fields that arise from field automorphisms of the mixed-characteristic local fields.

Citation

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Yuichiro Hoshi. "Topics in the anabelian geometry of mixed-characteristic local fields." Hiroshima Math. J. 49 (3) 323 - 398, November 2019. https://doi.org/10.32917/hmj/1573787035

Information

Received: 25 October 2017; Revised: 5 April 2019; Published: November 2019
First available in Project Euclid: 15 November 2019

zbMATH: 07180034
MathSciNet: MR4031737
Digital Object Identifier: 10.32917/hmj/1573787035

Subjects:
Primary: 11S20

Rights: Copyright © 2019 Hiroshima University, Mathematics Program

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Vol.49 • No. 3 • November 2019
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