Faltings' Theorem

Theorem

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

Then $C$ has only finitely many rational points.

Proof

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Also known as

Faltings' Theorem was originally known as Mordell's Conjecture, or the Mordell Conjecture.

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 who made it in $1922$.

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).

For this he was awarded the Fields Medal in $\text {1986}$.

Sources

• 1983: Gerd Faltings: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern (Inventiones Mathematicae Vol. 73, no. 3: pp. 349 – 366)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Mordell's conjecture
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Mordell's conjecture