Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Universität Rom III
Københavns Universitet
Universität Basel

Typ

Artikel

Journal

Selecta Mathematica, New Series

Band

29

ISSN

1022-1824

Publikationsdatum

21.01.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.), Physik und Astronomie (insg.)

Elektronische Version(en)

https://doi.org/10.1007/s00029-022-00823-w (Zugang: Offen)