Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE TATE-SHAFAREVICH GROUPS OVER BIQUADRATIC EXTENSIONS

  • Yu, Hoseog (Department of Mathematics, Sejong University)
  • Received : 2014.11.06
  • Accepted : 2014.12.10
  • Published : 2015.03.25
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Abstract

Let A be an abelian variety defined over a number field K. Let L be a biquadratic extension of K with Galois group G and let III (A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming III(A/L) is finite, we compute [III(A/K)]/[III(A/L)] where [X] is the order of a finite abelian group X.

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References

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