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ON THE TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ?

  • Received : 2010.09.24
  • Published : 2012.01.31

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

References

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Cited by

  1. ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR vol.50, pp.2, 2013, https://doi.org/10.4134/BKMS.2013.50.2.407