On Tate duality for Jacobian varieties.
Let \(k\) be a \(p\)-adic number field and let \(A(k)\) be an abelian variety over \(k\) with dual \(A^t(k)\). The author studies Tate's pairing \(A(k)\times H^1(k,A^t(k))\to \mathbb Q/\mathbb Z\) in the case that \(A=J\) is the Jacobian of a curve. He gives a description of the annihilator of \(U^nj(k)\) with respect to the Tate pairing, where \(\{U^nJ(k) | n=0,1,\dots\}\) is a filtration of \(J(k)\) given by the Néron model of \(J\).
scientific article; zbMATH DE number 1915507
scientific article