In algebraic geometry and number theory, the torsion conjecture states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. 1 Proposed Year1908 is Beppo Levi's proposal for the elliptic-curve case, later proven by Barry Mazur (1977-1978); the conjecture for general abelian varieties remains open. Progress Toward ResolutionCompletely resolved in the case of elliptic curves: Barry Mazur proved it over the rationals (1977, 1978) and Loic Merel over any number field (1996). 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Torsion Conjecture (Wikipedia)
Sources
1. Torsion Conjecture (Wikipedia)
Wikimedia FoundationLead section
Beppo Levi proposed the conjecture ... at the International Mathematical Congress in Rome
Elliptic curves
The torsion conjecture has been completely resolved in the case of elliptic curves.
Lead section, first sentence
the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field
In Branch: Number Theory, Lead sentence
In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian v
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