The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918468312367104 |
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| author | Sun, Zeming |
| author_facet | Sun, Zeming |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23485 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus Sun, Zeming Number Theory Algebraic Geometry 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. |
| title | The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2604.23485 |