Projects per year
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 language | English |
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Pages (from-to) | 4649-4660 |
Number of pages | 12 |
Journal | Proceedings of the American Mathematical Society |
Volume | 149 |
Issue number | 11 |
Early online date | 11 Jun 2021 |
DOIs | |
Publication status | Published - Nov 2021 |
Keywords
- Ax-Schanuel
- J-function
- Semiabelian variety
- Special variety
- Unlikely intersection
- Zilber-Pink
Projects
- 1 Finished
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Exponentially Algebraically closed fields.
Engineering and Physical Sciences Research Council
1/09/19 → 31/08/22
Project: Research