Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

authored by

Fabrizio Barroero, Lars Kühne, Harry Schmidt

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University Rome III
University of Copenhagen
University of Basel

Type

Article

Journal

Selecta Mathematica, New Series

Volume

29

ISSN

1022-1824

Publication date

21.01.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all), Physics and Astronomy(all)

Electronic version(s)

https://doi.org/10.1007/s00029-022-00823-w (Access: Open)