Bombieri–Lang conjecture

In arithmetic geometry, the Bombieri–Lang conjecture is an unproved conjecture about the rational points on an algebraic surface, named after Enrico Bombieri and Serge Lang. It states that, if ${\displaystyle X}$ is a smooth surface of general type defined over the rational numbers, then the rational points of ${\displaystyle X}$ do not form a dense set in the Zariski topology on ${\displaystyle X}$.