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ON THE TATE-SHAFAREVICH GROUPS OVER BIQUADRATIC EXTENSIONS

Yu, Hoseog

  • Received : 2014.11.06
  • Accepted : 2014.12.10
  • Published : 2015.03.25

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.

Keywords

Tate-Shafarevich group;abelian varieties;restriction of scalars

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