Abstract In 2002 Zilber, motivated by some model‐theoretical study of the formal theory of exponentiation, proposed a conjecture on ‘atypical’ intersections of subvarieties in tori. This conjecture, raised also independently by Bombieri, Masser and Zannier, and its generalization in the more general setting of mixed Shimura varieties due to Pink, led to the formulation of the so called problems of unlikely intersections , which have been intensively studied in the last three decades during which many important results in Diophantine Geometry have been proved. In this paper we will describe the conjecture about unlikely intersections in tori and in abelian varieties in different formulations, showing its connection with Schanuel's conjecture and we will review the state of the art on the subject.
Laura Capuano (2026) studied this question.