2019
Том 71
№ 11

# Tate-Shafarevich products in elliptic curves over pseudolocal fields with residue fields of characteristic 3

Andrychuk V. I.

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1057-1064.

Citation Example: 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.

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