On the Semi-absoluteness of Isomorphisms between the Pro- Arithmetic Fundamental Groups of Smooth Varieties
Shota Tsujimura
Kyoto University, Japan
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Abstract
Let be a prime number. In the present paper, we consider a certain pro- analogue of the semi-absoluteness of isomorphisms between the étale fundamental groups of smooth varieties over -adic local fields [i.e., finite extensions of the field of -adic numbers ] obtained by Mochizuki. This research was motivated by Higashiyama’s recent work on the pro- analogue of the semi-absolute version of the Grothendieck conjecture for configuration spaces [of dimension ] associated to hyperbolic curves over generalized sub--adic fields [i.e., subfields of finitely generated extensions of the completion of the maximal unramified extension of ].
Cite this article
Shota Tsujimura, On the Semi-absoluteness of Isomorphisms between the Pro- Arithmetic Fundamental Groups of Smooth Varieties. Publ. Res. Inst. Math. Sci. 59 (2023), no. 3, pp. 507–541
DOI 10.4171/PRIMS/59-3-3