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.
Original language | English |
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Article number | 18 |
Journal | Selecta Mathematica, New Series |
Volume | 29 |
Issue number | 2 |
Number of pages | 37 |
ISSN | 1022-1824 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:
© 2023, The Author(s).
- Heights, Semiabelian varieties, Unlikely intersections, Zilber–Pink conjecture
Research areas
ID: 382691408