Bull. Korean Math. Soc. 2013; 50(2): 407-416
Printed March 31, 2013
https://doi.org/10.4134/BKMS.2013.50.2.407
Copyright © The Korean Mathematical Society.
Dohyeong Kim
Pohang University of Science and Technology
Let $E$ be an elliptic curve over $\mathbb{Q}$ and $p$ be a prime of good supersingular reduction for $E$. Although the Iwasawa theory of $E$ over the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ 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 \cite{Kobayashi} and Pollack \cite{Pollack}, to give an explicit upper bound for the number of copies of $\mathbb{Q}_p/\mathbb{Z}_p$ occurring in the $p$-primary part of the Tate-Shafarevich group of $E$ over $\mathbb{Q}$.
Keywords: Iwasawa theory, supersingular prime, elliptic curves, Tate-Shafarevich group
MSC numbers: 11G05
2012; 49(1): 155-163
2023; 60(4): 1035-1059
2018; 55(3): 763-776
2009; 46(2): 303-309
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd