Glossary of Arithmetic and Diophantine Geometry - U

U

Uniformity conjecture

The unformity conjecture states that for any number field K and g > 2, there is a uniform bound B(g,K) on the number of K-rational points on any curve of genus g. The conjecture would follow from the Bombieri–Lang conjecture.

Unlikely intersection

An unlikely intersection is an algebraic subgroup intersecting a subvariety of a torus or abelian variety in a set of unusually large dimension, such as is involved in the Mordell-Lang_conjecture.