Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

Fabrizio Barroero ^[2] ; Lars Kühne ^[3] ; Harry Schmidt ^[1]
1. [1] University of Basel
  
  University of Basel
  
  Basilea, Suiza
2. [2] Università degli Studi Roma 3, Italy
3. [3] Universitetsparken 5, Denmark
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 2, 2023
Idioma: inglés
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Resumen
- 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.