Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR

  • Kim, Dohyeong (Department of Mathematics Pohang University of Science and Technology)
  • Received : 2011.03.09
  • Published : 2013.03.31
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Abstract

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 [5] and Pollack [8], 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 $\mathbb{Q}$.

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References

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