A curve of genus greater than one, defined over a number field, has only finitely many rational points. Proved by Gerd Faltings, it resolved the Mordell conjecture and won him a Fields Medal.
Facts
StatementA curve of genus greater than one defined over the rational numbers has only finitely many rational points. 1 Classification
Statement Form Connections
Sources
1. Faltings's Theorem (Wikipedia)
Wikimedia FoundationLead section, theorem statement
Curves of genus > 1 over the rationals have only finitely many rational points
Lead section, sentence dating Faltings's 1983 proof
known as the Mordell conjecture until its 1983 proof by Gerd Faltings
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