Elliptic Curves with Supersingular Reduction over $\Gamma$-extensions

TL;DR

This paper discusses formulas for the p-primary part of the Tate-Shafarevich group of elliptic curves with supersingular reduction over cyclotomic -extensions, extending understanding of their arithmetic properties.

Contribution

It provides explicit formulas for the Tate-Shafarevich group in the context of supersingular elliptic curves over -extensions, based on a translation of a 1976 research announcement.

Findings

Formulas for the p-primary part of Tate-Shafarevich groups

Application to elliptic curves with supersingular reduction

Insights into arithmetic over cyclotomic -extensions

Abstract

This is a translation of a research announcement by Anas G. Nasybullin from 1976, in which he states formulas for the p-primary part of the Tate-Shafarevich group of an elliptic curve in cyclotomic $\Z_p$-extensions of number fields.