# Faltings' Theorem

(Redirected from Mordell's Conjecture)

## Theorem

Let $C$ be a curve over $\Q$ of genus $g > 1$.

Then $C$ has only finitely many rational points.

## Source of Name

This entry was named for Gerd Faltings.

## Historical Note

The result now known as Faltings' Theorem was originally known as Mordell's Conjecture, after Louis Joel Mordell.

Gerd Faltings published a proof of it in his $1983$ paper: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern (Inventiones Mathematicae Vol. 73, no. 3: pp. 349 – 366).