Some remarks on atypical intersections

Aslanyan, Vahagn (2021) Some remarks on atypical intersections. Proceedings of the American Mathematical Society, 149 (11). pp. 4649-4660. ISSN 0002-9939

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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.

Item Type: Article
Uncontrolled Keywords: ax-schanuel,j-function,semiabelian variety,special variety,unlikely intersection,zilber-pink,mathematics(all),applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
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Depositing User: LivePure Connector
Date Deposited: 15 Jun 2021 00:08
Last Modified: 20 Apr 2023 21:33
DOI: 10.1090/proc/15611


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