2021/08/27 by Fabrizio Barroero, Barroero, Fabrizio, Lars Kühne +3 · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2108.12405
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.