On Tate duality for Jacobian varieties Original Research Article

Let A be an abelian variety over a p-adic field k and At its dual. The group of k-rational point A(k) has a p-adic decreasing filtration U·A(k). When A=J is a Jacobian variety, we give a precise description of the exact annihilator of UnA(k) with respect to the Tate pairing image. As an application, we give another proof of the result of McCallum in the special case A=J, which says that UnA(k) annihilates ker(H1(k,At)→H1(k′,At)) whenever k′/k is a finite extension of conductor less-than-or-equals, slantn.