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
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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).
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)