ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR

Title & Authors
ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR
Kim, Dohyeong;

Abstract
Let E be an elliptic curve over $\small{\mathbb{Q}}$ and $\small{p}$ be a prime of good supersingular reduction for E. Although the Iwasawa theory of E over the cyclotomic $\small{{\mathbb{Z}}_p}$-extension of $\small{\mathbb{Q}}$ is well known to be fundamentally different from the case of good ordinary reduction at p, we are able to combine the method of our earlier paper with the theory of Kobayashi [5] and Pollack [8], to give an explicit upper bound for the number of copies of $\small{{\mathbb{Q}}_p/{\mathbb{Z}}_p}$ occurring in the $\small{p}$-primary part of the Tate-Shafarevich group of E over $\small{\mathbb{Q}}$.
Keywords
Iwasawa theory;supersingular prime;elliptic curves;Tate-Shafarevich group;
Language
English
Cited by
References
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