Details
| Original language | English |
|---|---|
| Article number | 18 |
| Journal | Selecta Mathematica, New Series |
| Volume | 29 |
| Issue number | 2 |
| Publication status | Published - 21 Jan 2023 |
Abstract
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.
Keywords
- Heights, Semiabelian varieties, Unlikely intersections, Zilber–Pink conjecture
ASJC Scopus subject areas
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In: Selecta Mathematica, New Series, Vol. 29, No. 2, 18, 21.01.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Unlikely intersections of curves with algebraic subgroups in semiabelian varieties
AU - Barroero, Fabrizio
AU - Kühne, Lars
AU - Schmidt, Harry
N1 - 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.
PY - 2023/1/21
Y1 - 2023/1/21
N2 - 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.
AB - 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.
KW - Heights
KW - Semiabelian varieties
KW - Unlikely intersections
KW - Zilber–Pink conjecture
UR - http://www.scopus.com/inward/record.url?scp=85146660516&partnerID=8YFLogxK
U2 - 10.1007/s00029-022-00823-w
DO - 10.1007/s00029-022-00823-w
M3 - Article
AN - SCOPUS:85146660516
VL - 29
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
SN - 1022-1824
IS - 2
M1 - 18
ER -