English Dictionary

diophantine geometry

noun

(mathematics) 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.

Diophantine geometry is a branch of mathematics that deals with the study of Diophantine equations.

意味（1）

(mathematics) 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.

In this article, we shall recall how transcendence and diophantine geometry have grown into beautiful and far-reaching theories which now enhance many different aspects of mathematics, and we shall describe some of the principal problems that have emerged as a consequence of wide-ranging research in the field.