Some remarks on atypical intersections

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
4 Downloads (Pure)

Abstract

In this paper we show how some known weak forms of the Zilber-Pink conjecture can be strengthened by combining them with the Mordell-Lang conjecture or its variants. We illustrate this idea by proving some theorems on atypical intersections in the semiabelian and modular settings. Given a “finitely generated” set Γ with a certain structure, we consider Γ-special subvarieties-weakly special subvarieties containing a point of Γ-and show that every variety V contains only finitely many maximal Γ-atypical subvarieties, i.e. atypical intersections of V with Γ-special varieties the weakly special closures of which are Γ-special.

Original languageEnglish
Pages (from-to)4649-4660
Number of pages12
JournalProceedings of the American Mathematical Society
Volume149
Issue number11
Early online date11 Jun 2021
DOIs
Publication statusPublished - Nov 2021

Keywords

  • Ax-Schanuel
  • J-function
  • Semiabelian variety
  • Special variety
  • Unlikely intersection
  • Zilber-Pink

Cite this