Andrychuk V. I.
Tate-Shafarevich products in elliptic curves over pseudolocal fields with residue fields of characteristic 3
Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1157–1165
Let $k$ be a general local field with pseudolocal residue field $x$, char $x = 3$, and $A$ an elliptic curve defined over $k$. It is proved that the Tate-Shafarevich product $H^1(k, A)×A_k→ Q/ℤ$ of the group $H^1(k, A)$ of principal homogeneous spaces of the curve $A$ over $k$ and the group $A_k$ of its $k$-rational points is left nondegenerate.
The order and index of a principal homogeneous space for an elliptic curve over a general local field
Ukr. Mat. Zh. - 1975. - 27, № 1. - pp. 62–63