Rational points of the group of components of a Neron model

The structure of component groups of Neron models has been investigated on several occasions. Here we admit non-separably closed residue fields and are interested in the subgroup of rational points or, in other terms, in the subgroup of geometrically connected components of a Neron model. We consider Neron models of abelian varieties and of algebraic tori and give detailed computations in the case of Jacobians of curves.