The Semi-absolute Anabelian Geometry of Geometrically Pro- Arithmetic Fundamental Groups of Associated Low-Dimensional Configuration Spaces

  • Kazumi Higashiyama

    Kyoto University, Japan
The Semi-absolute Anabelian Geometry of Geometrically Pro-$p$ Arithmetic Fundamental Groups of Associated Low-Dimensional Configuration Spaces cover
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Abstract

Let be a prime number. In the present paper, we study geometrically pro- arithmetic fundamental groups of low-dimensional configuration spaces associated to a given hyperbolic curve over an arithmetic field such as a number field or a -adic local field. Our main results concern the group-theoretic reconstruction of the function field of certain tripods (i.e., copies of the projective line minus three points) that lie inside such a configuration space from the associated geometrically pro- arithmetic fundamental group, equipped with the auxiliary data constituted by the collection of decomposition groups determined by the closed points of the associated compactified configuration space.

Cite this article

Kazumi Higashiyama, The Semi-absolute Anabelian Geometry of Geometrically Pro- Arithmetic Fundamental Groups of Associated Low-Dimensional Configuration Spaces. Publ. Res. Inst. Math. Sci. 58 (2022), no. 3, pp. 579–634

DOI 10.4171/PRIMS/58-3-5