Raynaud, M. 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 Cited in 2 ReviewsCited in 49 Documents MSC: 14K20 Analytic theory of abelian varieties; abelian integrals and differentials 14L05 Formal groups, \(p\)-divisible groups 14K05 Algebraic theory of abelian varieties Keywords:torsion subgroup of Abelian variety; torsion point; Frobenius; indefinitely p-divisible element; rigid adherence Citations:Zbl 0518.00004 PDFBibTeX XML