The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus
Number Theory
2026-04-28 v1 Algebraic Geometry
Abstract
The objective of this paper is to further study the anabelian object referred to as \emph{pointed virtual curves}. Building upon previous work that investigated these fundamental-group-theoretic pullbacks of Galois sections in the genus-zero situation, we extend the central anabelian results to curves of arbitrary genus. To facilitate this generalization, we introduce the group-theoretic notion of an inclusion of CAVC-type and the categorical-theoretic notion of a virtual decuspidaloid. Furthermore, we establish a criterion regarding the "geometricity" of certain virtual curves, providing group-theoretic conditions under which a section of an arithmetic fundamental group arises from a rational point.
Cite
@article{arxiv.2604.23485,
title = {The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus},
author = {Zeming Sun},
journal= {arXiv preprint arXiv:2604.23485},
year = {2026}
}