Faltings' Theorem

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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).