mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, Raynaud's isogeny theorem, proved by , relates the

Faltings height A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic ...

s of two isogeneous

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

References

* Elliptic curves Theorems in algebraic geometry {{numtheory-stub