Meaning of diophantine geometry | Babel Free

Definitions

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.

Examples

“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.”

“This reflects the general principle in Diophantine geometry that in attempting to study any significant problem, it is essential to have a thorough understanding of the geometry before one can hope to make progress on the number theory.”

“The topics of the talks extended from algebraic number theory to diophantine geometry, curves and abelian varieties over finite fields and applications to codes, boolean functions or cryptography.”

CEFR level