About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 - Andriichuk , V. I. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Let$k$ be a general local field with pseudolocal residue field $κ$, ${\rm char} κ = 3$, and $А$ an elliptic curve defined over $k$. It is proved that the Tate-Shafarevich product $H^1(k, A) × A_k→ Q/ \mathbb Z$ of the group $H^1 (k, А)$ of principal homogeneous spaces of the curve $А$ over $ k$ and the group $А_к$ of its $k$-rational points is left nondegenerate.