Unlikely intersections of curves with algebraic subgroups in semiabelian varieties
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Let G be a semiabelian variety and C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over Q¯. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.
| Originalsprog | Engelsk |
|---|---|
| Artikelnummer | 18 |
| Tidsskrift | Selecta Mathematica, New Series |
| Vol/bind | 29 |
| Udgave nummer | 2 |
| Antal sider | 37 |
| ISSN | 1022-1824 |
| DOI | |
| Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:
The authors thank the referee for carefully reading the paper and providing several suggestions that significantly improved the article. They moreover thank thank Éric Gaudron and Philipp Habegger for comments and feedback. FB was supported by the Swiss National Science Foundation Grant 165525. LK was supported by an Ambizione Grant of the Swiss National Science Foundation. LK also received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 101027237.
Publisher Copyright:
© 2023, The Author(s).
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