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arithmetic of abelian varieties
In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as elliptic curves; and has become a very substantial area both in terms of results and conjectures. Most of these can be posed for an abelian variety ''A'' over a number field ''K''; or more generally (for global fields or more general finitely-generated rings or fields).
==Integer points on abelian varieties==
There is some tension here between concepts: ''integer point'' belongs in a sense to affine geometry, while ''abelian variety'' is inherently defined in projective geometry. The basic results proving that elliptic curves have finitely many integer points come out of diophantine approximation.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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