On the local norm map for abelian varieties with good ordinary reduction (Q1174742)

Let \(A\) be an abelian variety defined over \(K\), a finite extension of \(\mathbb{Q}_ p\), and \(L/K\) a Galois extension whose Galois group is isomorphic to the additive group \(\mathbb{Z}_ p\). The cokernel of \(A(K)\) by the universal norms for the extension \(L/K\) is important in the Iwasawa theory of \(A\). The order of this quotient was first calculated by \textit{P. Schneider} [Invent. Math. 71, 251-293 (1983; Zbl 0511.14010)] when \(A\) has good ordinary reduction at \(p\). This paper gives a second proof of his result using less sophisticated machinery.