Weil restriction and Grothendieck's duality conjecture

Let A, A' be dual abelian varieties over a field K, which is the field of fractions of a discrete valuation ring R with residue field k. In this paper we use the technique of Weil restriction to investigate Grothendieck's pairing on the component groups of the N\ue9ron models of A,A, with particular attention to the case of non perfect k. Important results are counterexamples to the perfectness of the pairing in the case of non perfect residue field. In general we show that the pairing is perfect as soon as it is perfect after a tamely ramified extension with trivial residue extension