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Sous-variétés d’une variété abélienne et points de torsion. (French) Zbl 0581.14031
Arithmetic and geometry, Pap. dedic. I. R. Shafarevich, Vol. I: Arithmetic, Prog. Math. 35, 327-352 (1983).
[For the entire collection see Zbl 0518.00004.]
Let A be an abelian variety defined over the complex number field, T the torsion subgroup of A and X an integrally closed subscheme of A. Then the main theorem is: ”If \(T\cap X\) is dense in X in the sense of Zariski topology, then X is a translation of an abelian subvariety of A with respect to a torsion point”. For a more precise statement, see theorem 3.5.1 and its corollary 3.5.2.
Reviewer: K.Katayama

MSC:
14K20 Analytic theory of abelian varieties; abelian integrals and differentials
14L05 Formal groups, \(p\)-divisible groups
14K05 Algebraic theory of abelian varieties