About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3

Abstract

Let$k$  be a general local field with pseudolocal residue field $\kappa$, ${\rm char} \kappa = 3$, and $А$  an elliptic curve defined over $k$. It is proved that the Tate-Shafarevich product $H^1(k, A) \times A_k→ Q/ \mathbb Z$  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.