complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group...
21 KB (2,918 words) - 10:20, 25 April 2024
mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field k. A 1-dimensional abelian variety is an elliptic curve...
10 KB (1,609 words) - 10:33, 25 April 2024
mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the...
7 KB (904 words) - 13:45, 13 January 2022
Abelian varieties are a natural generalization of elliptic curves, including algebraic tori in higher dimensions. Just as elliptic curves have a natural...
5 KB (761 words) - 14:33, 27 September 2023
In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces...
5 KB (648 words) - 11:37, 19 December 2022
Hodge conjecture (section Abelian varieties)
conjecture holds for sufficiently general abelian varieties, for products of elliptic curves, and for simple abelian varieties of prime dimension. However, Mumford...
22 KB (2,983 words) - 16:17, 17 August 2024
In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how "bad" the bad...
4 KB (663 words) - 17:56, 7 July 2020
This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves. 3rd century AD Diophantus of Alexandria studies...
10 KB (1,050 words) - 23:35, 10 June 2024
Jacobian variety is an example of an abelian variety, a complete variety with a compatible abelian group structure on it (the name "abelian" is however...
41 KB (5,759 words) - 22:50, 17 June 2024
component of the identity in the Picard group of C, hence an abelian variety. The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete...
7 KB (805 words) - 19:27, 14 March 2024