Geodesic
On elliptic curves over pseudolocal fields
Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 83-94

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In this paper it is shown that for pseudolocal fields there is a natural analog of the Tate–Shafarevich duality for elliptic curves, taking the following form: Theorem. If $A$ is an elliptic curve defined over the pseudolocal field $k$, whose residue field has characteristic not equal to $2$ or $3$, then the Tate–Shafarevich pairing $$ H^1(k,A)\times A_k\to Q/Z $$ is left nondegenerate. Bibliography: 11 titles. 
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     title = {On elliptic curves over pseudolocal fields},
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V. I. Andriichuk. On elliptic curves over pseudolocal fields. Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 83-94. http://geodesic.mathdoc.fr/item/SM_1981_38_1_a5/