On the Notion of Visibility of Torsors

Abstract

AbstractLet J be an abelian variety and A be an abelian subvariety of J , both defined over Q. Let x be an element of H 1(Q; A ). Then there are at least two definitions of x being visible in J : one asks that the torsor corresponding to x be isomorphic over Q to a subvariety of J , and the other asks that x be in the kernel of the natural map H1 (Q;A ) → H 1(Q; J ). In this article, we clarify the relation between the two definitions.