Some remarks on atypical intersections

Vahagn Aslanyan

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    2 Citations (Scopus)
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    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

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