A developing branch of mathematics in which techniques of algebraic geometry are applied to number theory, in particular being concerned with schemes of finite type over the spectrum of the ring of integers, Spec(ℤ). Wiktionary

Branch of mathematics. Wiktionary (translation)

A developing branch of mathematics in which techniques of algebraic geometry are applied to number theory (specifically the theory of Diophantine equations), in particular being concerned with algebraic varieties over fields that are finitely generated over their prime fields and over local fields. Wiktionary