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Title: On the Semi-absoluteness of Isomorphisms between the Pro-$p$ Arithmetic Fundamental Groups of Smooth Varieties over $p$-adic Local Fields
Authors: TSUJIMURA, Shota
Author's alias: 辻村, 昇太
Keywords: 14H30
anabelian geometry
étale fundamental group
hyperbolic curve
configuration space
p-adic local field
pro-p Grothendieck Conjecture
Issue Date: Oct-2020
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Start page: 1
End page: 34
Thesis number: RIMS-1930
Abstract: Let p be a prime number. In the present paper, we consider a certain pro-p analogue of the semi-absoluteness of isomorphisms between the étale fundamental groups of smooth varieties over p-adic local fields [i.e., finite extensions of the field of p-adic numbers Qp] obtained by Mochizuki. This research was motivated by Higashiyama's recent work on the pro-p analogue of the semi-absolute version of the Grothendieck Conjecture for configuration spaces [of dimension ≥2] associated to hyperbolic curves over generalized sub-p-adic fields [i.e., subfields of finitely generated extensions of the completion of the maximal unramified extension of Qp].
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