On the Tate-Shafarevich group of elliptic curves over $\mathbb Q$
Bull. Korean Math. Soc. 2012 Vol. 49, No. 1, 155-163
https://doi.org/10.4134/BKMS.2012.49.1.155
Published online January 1, 2012
Dohyeong Kim
Pohang University of Science and Technology
Abstract : Let $E$ be an elliptic curve over $\mathbb Q$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the $p$-adic $L$-function at $s=0$, and the $\mathbb Z_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes $p$.
Keywords : good ordinary reduction, Tate-Shafarevich group, elliptic curves, Iwasawa theory
MSC numbers : 11G05
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