Glossary of Arithmetic and Diophantine Geometry - M

M

Mordell conjecture

The Mordell conjecture is now the Faltings theorem, and states that a curve of genus at least two has only finitely many rational points. The Uniformity conjecture states that there should be a uniform bound on the number of such points, depending only on the genus and the field of definition.

Mordell–Lang conjecture

The Mordell–Lang conjecture is a collection of conjectures of Serge Lang unifying the Mordell conjecture and Manin–Mumford conjecture in an abelian variety or semi-abelian variety.

Mordell–Weil theorem

The Mordell–Weil theorem is a foundational result stating that for an abelian variety A over a number field K the group A(K) is a finitely-generated abelian group. This was proved initially for number fields K, but extends to all finitely-generated fields.

Modellic variety

A Mordellic variety is an algebraic variety which has only finitely many points in any finitely generated field.