Work

Some remarks on atypical intersections

Year: 2021

Type: article

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 \Gamma with a certain structure, we consider Γ \Gamma -special subvarieties—weakly special subvarieties containing a point of Γ \Gamma —and show that every variety V V contains only finitely many maximal Γ \Gamma -atypical subvarieties, i.e. atypical intersections of V V with Γ \Gamma -special varieties the weakly special closures of which are Γ \Gamma -special.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/15611

Author: Vahagn Aslanyan

Institutions: University of East Anglia, Carnegie Mellon University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Carnegie Mellon University, University of East Anglia, Engineering and Physical Sciences Research Council

Awards: G1096181028, Exponentially Algebraically Closed Fields