Existence of global Néron models beyond semi-abelian varieties

We first prove Bosch-Lütkebohmert-Raynaud’s conjectures on existence of global Néron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the imperfect residue fields case. Finally, as a complement to the conjectures, we classify unirational wound unipotent groups “up to relative perfection”, again in the perfect residue fields case. The key ingredient for all these is the duality for relatively perfect unipotent groups.