# Faltings' Theorem

(Redirected from Mordell's Conjecture)

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## Theorem

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

Then $C$ has only finitely many rational points.

## Proof

## 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).

## Sources

- 1983: Gerd Faltings:
*Endlichkeitssätze für abelsche Varietäten über Zahlkörpern*(*Inventiones Mathematicae***Vol. 73**,*no. 3*: pp. 349 – 366)