Diophantine geometry
| Geometry |
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| Geometers |
In mathematics, Diophantine geometry is the study of Diophantine equations (the search for integer solutions of polynomial equations) by means of powerful methods in algebraic geometry. The extensive development of algebraic geometry in the 20th century produced powerful tools to study these equations. Diophantine geometry is part of the broader field of arithmetic geometry.
Four theorems of fundamental importance in Diophantine geometry are:
- Mordell–Weil theorem
- Roth's theorem
- Siegel's theorem
- Faltings' theorem
Another major theorem is Mazur's torsion theorem. More modern examples include the André–Oort conjecture, the Bogomolov conjecture and also the uniform Mordell conjecture.