Word.ws English Dictionary

diophantine geometry

diophantine geometry noun: 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.

Noun

diophantine geometry

  1. 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...2000, A. Baker, G. Wüstholz, “Number Theory, Transcendence and Diophantine Geometry in the Next Millennium”, in V. Arnold, M. Atiyah, P. Lax, B. Mazur, editors, Mathematics: Frontiers and...
    • 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.2009, Joseph H. Silverman, The Arithmetic of Elliptic Curves, 2nd edition, Springer, page 41

Forms of diophantine geometry

alternative formDiophantine geometry

Questions about diophantine geometry

What does diophantine geometry mean?
Diophantine geometry means 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.
What part of speech is diophantine geometry?
Diophantine geometry is a noun.

Words near diophantine geometry in the dictionary

  1. dioperad
  2. dioperads
  3. diophantine
  4. Diophantine equation
  5. Diophantine equations
  6. diophantine geometry
  7. Diophantus
  8. Diophysite
  9. Diophysites
  10. Diophysitism
  11. Diops

Source and license

Adapted from Wiktionary: diophantine geometry (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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