Product of local points of subvarieties of almost isotrivial semi-abelian varieties over a global function field

Abstract

For a semi-abelian variety over a global function field which is isogenous to an isotrivial one, we show that on the product of local points of a subvariety satisfying a minor condition, the topological closure of a finitely generated subgroup of %the group of its global points cuts out exactly the global points of the subvariety lying in this subgroup. As a corollary, on every non-isotrivial super-singular curve of genus two over a global function field, we conclude that the Brauer-Manin condition cuts out exactly the set of its rational points.