On local ``class fields'' of elliptic curves

O. N. Vvedenskii

Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 19-84.

Résumé

In this paper a method is given for computing the Tate–Shafarevich pairing on elliptic curves for simple cyclic extensions. With this foundation the properties of the Tate–Shafarevich pairing are investigated over both a local field and a general local field of definition.

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