diophantine geometry

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(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.

日本語の意味

ディオファントス幾何学：代数幾何学の技法をディオファントス方程式や、素体上または局所体上で有限生成された体上の代数多様体に適用し、数論（特に整数解の問題）を研究する発展途上の数学分野

英語の意味

(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.

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Recent breakthroughs in diophantine geometry have deepened our understanding of rational points on algebraic varieties.

ディオファントス幾何学の最近の進展は、代数多様体上の有理点に関する私たちの理解を深めた。

詳細

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.

詳細